bayesian_analysis_20201206
library(tidyverse)
library(psych)
library(rstan) # to run the Bayesian model (stan)
library(coda) # to obtain HPD intervals (HPDinterval)
library(mvtnorm) # to generate random correlated data (rmvnorm)
library(car) # to plot the inferred distribution (dataEllipse)
library(brms)
library(bayesplot)
library(gridExtra)
options(mc.cores = parallel::detectCores())
options (error=recover)
library(foreign) # to read SPSS file
data <- here::here('1. Data/1. WA project (SPSS)-2019-6-11.sav') %>%
read.spss(to.data.frame=TRUE)
data <- data[,-2]
source("2_Rcodes_2020-09-18/rob.cor.mcmc_additional_criteria.R")
data$Rawfreq <- log(data$Rawfreq)
data$Raw_first <- log(data$Raw_first)
data$RawFirst <- log(data$RawFirst)
attach(data)
head(data)## ID Nativelikeness Comp Lex30raw Lex30 Numberofresp Rawfreq tscore
## 1 111 7.538462 6.384615 41 43.158 104 6.282870 6.970751
## 2 112 6.230769 5.076923 35 40.697 108 5.984021 8.793760
## 3 113 6.384615 6.769231 33 36.667 109 6.569201 8.210262
## 4 114 7.230769 6.923077 30 30.928 108 6.047171 8.213042
## 5 115 7.307692 6.384615 22 30.986 95 6.382420 7.441458
## 6 116 6.230769 7.307692 34 44.156 101 6.265812 8.155772
## MI MI2 LogDice Raw_first tscore_first MI_first MI2_first
## 1 1.910758 8.469356 2.860707 6.081403 7.618452 2.485408 9.393354
## 2 1.985217 8.518691 2.810504 6.347457 9.508932 2.263757 8.956739
## 3 1.616796 8.709225 3.257821 6.962454 9.602330 1.688280 8.868220
## 4 1.608021 8.559300 3.163457 5.791183 9.877567 2.006507 9.066217
## 5 1.256642 8.087881 3.031709 7.093374 10.084976 1.164878 8.145006
## 6 1.555219 8.103584 2.897684 6.393533 6.363937 1.373691 7.789863
## LogDice_first t_cutoff_2 MI_cutoff_0 MI_cutoff_2 MI_cutoff_3 LD_cutoff_2
## 1 3.328366 0.6250000 0.7211538 0.3557692 0.2884615 0.6346154
## 2 3.048217 0.6203704 0.7129630 0.3518519 0.2222222 0.5462963
## 3 3.415265 0.6238532 0.7155963 0.2844037 0.2110092 0.6055046
## 4 3.413932 0.5555556 0.7314815 0.3333333 0.1944444 0.6388889
## 5 3.105427 0.5473684 0.6315789 0.2842105 0.2000000 0.6315789
## 6 2.753349 0.5940594 0.7029703 0.3465347 0.2475248 0.6237624
## tscore.2 tscore.10 MI.3 MI.7 Logdicegt7 DiversityMTLD
## 1 0.6250000 0.2500000 0.2884615 0.009615385 0.01923077 43.653
## 2 0.6203704 0.2777778 0.2222222 0.009259259 0.01851852 32.680
## 3 0.6238532 0.2385321 0.2110092 0.000000000 0.03669725 27.980
## 4 0.5555556 0.2962963 0.1944444 0.000000000 0.02777778 19.200
## 5 0.5473684 0.2631579 0.2000000 0.000000000 0.01052632 25.351
## 6 0.5940594 0.2376238 0.2475248 0.000000000 0.02970297 26.901
## FrequencyJACETInfrequentwordratio WordCount COCA_spoken_Range_Log_AW
## 1 0.10638298 74 -0.4132691
## 2 0.08333333 82 -0.3847393
## 3 0.09090909 141 -0.3543852
## 4 0.10810811 93 -0.3621051
## 5 0.00000000 94 -0.3030986
## 6 0.02439024 74 -0.2600043
## COCA_spoken_Frequency_Log_AW COCA_spoken_Bigram_Frequency_Log
## 1 3.075455 1.423177
## 2 3.157143 1.452227
## 3 3.242869 1.573254
## 4 3.306088 1.635040
## 5 3.236288 1.354882
## 6 3.357921 1.484601
## COCA_spoken_Bigram_Range_Log COCA_spoken_Trigram_Frequency_Log
## 1 -1.339891 0.6517929
## 2 -1.340273 0.4822114
## 3 -1.236915 0.5668987
## 4 -1.202289 0.4332461
## 5 -1.397088 0.2487292
## 6 -1.292880 0.4127399
## COCA_spoken_Trigram_Range_Log IndexCOCA_spoken_Frequency_Log_AW FAC1_1
## 1 -2.015825 1.607021 -0.29832644
## 2 -2.175634 1.523029 0.01254624
## 3 -2.082042 1.910392 1.02337270
## 4 -2.225078 1.823994 1.67592462
## 5 -2.388899 1.903294 -0.54963879
## 6 -2.227538 1.882117 0.44157937
## FAC2_1 FAC3_1 RawFirst RawSecond RawThird RawFourth T_First
## 1 0.5145524 -0.8557059 6.081403 146.6250 1091.6522 494.6667 7.618452
## 2 -0.8784494 -0.1260386 6.347457 288.0435 431.6087 231.5882 9.508932
## 3 -0.1905995 0.7445929 6.962454 645.1667 534.5455 543.3636 9.602330
## 4 -1.4208401 0.9929462 5.791183 455.8148 428.5455 491.7000 9.877567
## 5 -2.6610871 1.1167707 7.093374 250.5600 381.9474 280.4615 10.084976
## 6 -1.3281218 2.3686025 6.393533 686.4643 389.6087 263.0769 6.363937
## T_Second T_Third T_Fourth MI_First1 MI_Second MI_Third MI_Fourth Richness
## 1 4.678420 5.889352 10.401449 2.485408 1.660840 1.361889 2.051415 0.3712
## 2 6.756471 11.396671 6.934716 2.263757 1.409582 2.347246 1.848211 0.1938
## 3 8.612824 6.567567 7.705351 1.688280 1.302220 1.531392 1.957641 0.3886
## 4 8.107667 5.619153 9.127916 2.006507 1.428980 1.205301 1.794612 0.2838
## 5 6.199212 6.685346 5.445098 1.164878 1.271848 1.507015 1.052054 0.2210
## 6 9.275682 9.772509 6.880444 1.373691 1.583914 1.878349 1.326667 0.1952
## MTLD Fluency ArticulationRate FilledPause SilentPause invertedRawFreq
## 1 43.653 0.4408 85.23792 0.21621622 0.8783784 -535.3226
## 2 32.680 0.3126 62.73555 0.06097561 0.7439024 -397.0337
## 3 27.980 0.4506 138.67348 0.01418440 0.5390071 -712.8000
## 4 19.200 0.2978 93.89826 0.02150538 0.6451613 -422.9149
## 5 25.351 0.3328 73.65811 0.19148936 0.8936170 -591.3571
## 6 26.901 0.2382 73.79596 0.02702703 0.9189189 -526.2688
## invertedFirstRawFreq
## 1 -437.6429
## 2 -571.0385
## 3 -1056.2222
## 4 -327.4000
## 5 -1203.9630
## 6 -597.9655iter1 = 5000
iter2 = 9000
IC_plot <- function(obj_compare_loo, metric) {
data <- as.data.frame(obj_compare_loo[, 7:8])
names(data)[1] <- "ic" ## change name so that any info criterion can be plotted
names(data)[2] <- "se"
plot <- data %>%
data.frame() %>%
rownames_to_column(var = "model_name") %>%
ggplot(aes(x = model_name,
y = ic,
ymin = ic - se,
ymax = ic + se)) +
geom_pointrange(shape = 21) +
coord_flip() +
labs(x = NULL, y = metric) +
theme_classic() +
theme(text = element_text(family = "Courier"),
axis.ticks.y = element_blank(),
panel.background = element_rect())
return(plot)
}
model_comp <- function(Null_Model, Model_1, Model_2) {
Null_Model <- add_criterion(Null_Model, criterion = c("loo", "waic"))
Model_1 <- add_criterion(Model_1, criterion = c("loo", "waic"))
Model_2 <- add_criterion(Model_2, criterion = c("loo", "waic"))
loos <- loo_compare(Null_Model, Model_1, Model_2, criterion = "loo")
waics <- loo_compare(Null_Model, Model_1, Model_2, criterion = "waic")
loo_plot <- IC_plot(loos, "looic")
waic_plot <- IC_plot(waics, "waic")
return(list(as.data.frame(loos), as.data.frame(waics), loo_plot, waic_plot))
}
posterior_scatter <- function(model, xaxis, yaxis) {
x = deparse(substitute(xaxis))
y = deparse(substitute(yaxis))
x.rand = as.data.frame(extract(model, c("x_rand"))[[1]])
p <- ggplot(data, aes(x = xaxis, y = yaxis)) +
geom_point() +
stat_ellipse(x.rand, mapping = aes(V2, V1), type = 't', level = .95, fill ="#56B4E9", geom = 'polygon', alpha = .2) +
stat_ellipse(x.rand, mapping = aes(V2, V1), type = 't', level = .5, fill ="#56B4E9", geom = 'polygon', alpha = .4) +
theme_bw() +
labs(caption = "Note. Points show the sample data points; The ellipses show the areas within which 50 and 95% of posterior draws fall.", x = x , y = y)
return(p)
}
very_weak_prior <- c(
prior(student_t(3, 0, 10), class = b)
)
very_weak_prior_cauchy <- c(
prior(student_t(3, 0, 10), class = Intercept),
prior(student_t(3, 0, 10), class = b),
prior(cauchy(0, 10), class = sigma)
)
weak_prior <- c(
prior(student_t(3, 0, 1), class = b)
)
weak_prior_cauchy <- c(
prior(student_t(3, 0, 10), class = Intercept),
prior(student_t(3, 0, 1), class = b),
prior(cauchy(0, 10), class = sigma)
)sessionInfo()## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.7
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] foreign_0.8-75 gridExtra_2.3 bayesplot_1.7.2
## [4] brms_2.13.5 Rcpp_1.0.5 car_3.0-9
## [7] carData_3.0-4 mvtnorm_1.1-1 coda_0.19-4
## [10] rstan_2.21.2 StanHeaders_2.21.0-6 psych_2.0.9
## [13] forcats_0.5.0 stringr_1.4.0 dplyr_1.0.2
## [16] purrr_0.3.4 readr_1.3.1 tidyr_1.1.2
## [19] tibble_3.0.4 ggplot2_3.3.2 tidyverse_1.3.0
##
## loaded via a namespace (and not attached):
## [1] TH.data_1.0-10 colorspace_2.0-0 ellipsis_0.3.1
## [4] rio_0.5.16 ggridges_0.5.2 rprojroot_2.0.2
## [7] rsconnect_0.8.16 estimability_1.3 markdown_1.1
## [10] base64enc_0.1-3 fs_1.5.0 rstudioapi_0.13
## [13] DT_0.16 fansi_0.4.1 lubridate_1.7.9
## [16] xml2_1.3.2 splines_3.6.3 bridgesampling_1.0-0
## [19] codetools_0.2-16 mnormt_1.5-7 knitr_1.30
## [22] shinythemes_1.1.2 jsonlite_1.7.2 broom_0.7.0
## [25] dbplyr_1.4.4 shiny_1.5.0 compiler_3.6.3
## [28] httr_1.4.2 emmeans_1.5.3 backports_1.1.10
## [31] assertthat_0.2.1 Matrix_1.2-18 fastmap_1.0.1
## [34] cli_2.2.0 later_1.1.0.1 htmltools_0.5.0
## [37] prettyunits_1.1.1 tools_3.6.3 igraph_1.2.5
## [40] gtable_0.3.0 glue_1.4.2 reshape2_1.4.4
## [43] V8_3.2.0 cellranger_1.1.0 vctrs_0.3.5
## [46] nlme_3.1-144 crosstalk_1.1.0.1 xfun_0.19
## [49] ps_1.5.0 openxlsx_4.1.5 rvest_0.3.6
## [52] miniUI_0.1.1.1 mime_0.9 lifecycle_0.2.0
## [55] gtools_3.8.2 MASS_7.3-51.5 zoo_1.8-8
## [58] scales_1.1.1 colourpicker_1.0 hms_0.5.3
## [61] promises_1.1.1 Brobdingnag_1.2-6 sandwich_2.5-1
## [64] parallel_3.6.3 inline_0.3.16 shinystan_2.5.0
## [67] yaml_2.2.1 curl_4.3 loo_2.3.1
## [70] stringi_1.5.3 dygraphs_1.1.1.6 pkgbuild_1.1.0
## [73] zip_2.1.1 rlang_0.4.9 pkgconfig_2.0.3
## [76] matrixStats_0.57.0 evaluate_0.14 lattice_0.20-38
## [79] rstantools_2.1.1.9000 htmlwidgets_1.5.3 processx_3.4.5
## [82] tidyselect_1.1.0 here_0.1 plyr_1.8.6
## [85] magrittr_2.0.1 R6_2.5.0 generics_0.1.0
## [88] multcomp_1.4-14 DBI_1.1.0 pillar_1.4.7
## [91] haven_2.3.1 withr_2.3.0 xts_0.12-0
## [94] survival_3.2-7 abind_1.4-5 modelr_0.1.8
## [97] crayon_1.3.4 rmarkdown_2.3 grid_3.6.3
## [100] readxl_1.3.1 data.table_1.12.8 blob_1.2.1
## [103] callr_3.5.1 threejs_0.3.3 reprex_0.3.0
## [106] digest_0.6.27 xtable_1.8-4 httpuv_1.5.4
## [109] RcppParallel_5.0.2 stats4_3.6.3 munsell_0.5.0
## [112] shinyjs_1.1describe(data)## vars n mean sd median trimmed mad
## ID 1 40 214.40 71.74 211.50 214.47 134.92
## Nativelikeness 2 40 5.40 1.34 5.58 5.46 1.43
## Comp 3 40 4.84 1.59 4.92 4.91 1.82
## Lex30raw 4 40 45.30 10.53 45.00 45.50 11.12
## Lex30 5 40 44.21 7.49 43.87 44.12 8.25
## Numberofresp 6 40 110.25 7.88 112.00 111.28 5.93
## Rawfreq 7 40 5.92 0.34 5.99 5.92 0.41
## tscore 8 40 7.49 1.93 7.69 7.48 2.04
## MI 9 40 1.82 0.33 1.82 1.82 0.33
## MI2 10 40 8.35 0.59 8.45 8.35 0.56
## LogDice 11 40 2.87 0.34 2.88 2.88 0.37
## Raw_first 12 40 5.98 0.57 5.90 5.94 0.63
## tscore_first 13 40 8.63 3.36 8.42 8.49 3.24
## MI_first 14 40 2.02 0.48 2.04 2.02 0.51
## MI2_first 15 40 8.72 0.93 8.91 8.69 0.97
## LogDice_first 16 40 3.08 0.54 3.10 3.07 0.55
## t_cutoff_2 17 40 0.58 0.09 0.60 0.57 0.08
## MI_cutoff_0 18 40 0.68 0.08 0.68 0.67 0.07
## MI_cutoff_2 19 40 0.36 0.07 0.35 0.36 0.07
## MI_cutoff_3 20 40 0.25 0.06 0.24 0.25 0.05
## LD_cutoff_2 21 40 0.58 0.08 0.60 0.58 0.08
## tscore.2 22 40 0.58 0.09 0.60 0.57 0.08
## tscore.10 23 40 0.26 0.06 0.25 0.25 0.06
## MI.3 24 40 0.25 0.06 0.24 0.25 0.05
## MI.7 25 40 0.01 0.01 0.01 0.01 0.01
## Logdicegt7 26 40 0.02 0.01 0.02 0.02 0.01
## DiversityMTLD 27 40 37.09 10.21 36.92 36.76 12.83
## FrequencyJACETInfrequentwordratio 28 40 0.08 0.03 0.09 0.08 0.03
## WordCount 29 40 120.45 39.74 113.50 118.12 34.10
## COCA_spoken_Range_Log_AW 30 40 -0.38 0.05 -0.37 -0.38 0.04
## COCA_spoken_Frequency_Log_AW 31 40 3.16 0.09 3.17 3.17 0.07
## COCA_spoken_Bigram_Frequency_Log 32 40 1.46 0.11 1.47 1.46 0.14
## COCA_spoken_Bigram_Range_Log 33 40 -1.33 0.10 -1.33 -1.33 0.10
## COCA_spoken_Trigram_Frequency_Log 34 40 0.59 0.12 0.56 0.59 0.13
## COCA_spoken_Trigram_Range_Log 35 40 -2.07 0.11 -2.09 -2.07 0.12
## IndexCOCA_spoken_Frequency_Log_AW 36 40 1.64 0.14 1.62 1.64 0.16
## FAC1_1 37 40 0.00 1.00 0.06 0.00 1.07
## FAC2_1 38 40 0.00 1.00 -0.21 0.00 1.06
## FAC3_1 39 40 0.00 1.00 0.10 0.08 0.86
## RawFirst 40 40 5.98 0.57 5.90 5.94 0.63
## RawSecond 41 40 396.85 232.65 320.90 379.02 231.12
## RawThird 42 40 360.47 214.31 339.50 333.08 162.22
## RawFourth 43 40 324.07 161.08 277.69 304.73 97.66
## T_First 44 40 8.63 3.36 8.42 8.49 3.24
## T_Second 45 40 7.74 3.04 7.59 7.66 2.46
## T_Third 46 40 6.92 2.57 6.91 6.98 2.08
## T_Fourth 47 40 6.29 3.25 6.87 6.48 2.18
## MI_First1 48 40 2.02 0.48 2.04 2.02 0.51
## MI_Second 49 40 1.82 0.48 1.81 1.82 0.56
## MI_Third 50 40 1.75 0.45 1.67 1.73 0.39
## MI_Fourth 51 40 1.66 0.57 1.80 1.70 0.63
## Richness 52 40 0.42 0.12 0.44 0.42 0.12
## MTLD 53 40 37.09 10.21 36.92 36.76 12.83
## Fluency 54 40 0.52 0.17 0.51 0.52 0.22
## ArticulationRate 55 40 109.12 26.62 107.95 108.73 25.60
## FilledPause 56 40 0.07 0.06 0.05 0.06 0.05
## SilentPause 57 40 0.60 0.21 0.56 0.59 0.21
## invertedRawFreq 58 40 -394.23 129.28 -397.70 -386.18 165.60
## invertedFirstRawFreq 59 40 -466.11 294.68 -366.30 -413.67 223.64
## min max range skew kurtosis se
## ID 111.00 318.00 207.00 0.01 -1.19 11.34
## Nativelikeness 2.00 7.54 5.54 -0.43 -0.69 0.21
## Comp 1.38 7.31 5.92 -0.31 -1.01 0.25
## Lex30raw 22.00 65.00 43.00 -0.09 -0.86 1.67
## Lex30 30.93 61.91 30.98 0.19 -0.73 1.18
## Numberofresp 85.00 120.00 35.00 -1.17 1.07 1.25
## Rawfreq 5.30 6.57 1.27 -0.09 -1.25 0.05
## tscore 4.10 12.30 8.20 0.07 -0.51 0.30
## MI 1.19 2.60 1.41 0.00 -0.60 0.05
## MI2 7.17 9.49 2.31 -0.05 -0.87 0.09
## LogDice 2.16 3.47 1.31 -0.26 -0.85 0.05
## Raw_first 5.14 7.15 2.01 0.38 -0.82 0.09
## tscore_first 1.93 17.04 15.11 0.28 -0.46 0.53
## MI_first 1.16 3.25 2.08 0.12 -0.47 0.08
## MI2_first 7.10 10.94 3.84 0.17 -0.65 0.15
## LogDice_first 1.90 4.32 2.42 0.04 -0.53 0.09
## t_cutoff_2 0.44 0.78 0.34 0.10 -0.74 0.01
## MI_cutoff_0 0.54 0.85 0.31 0.09 -0.57 0.01
## MI_cutoff_2 0.26 0.50 0.24 0.47 -0.63 0.01
## MI_cutoff_3 0.15 0.36 0.22 0.29 -0.55 0.01
## LD_cutoff_2 0.39 0.71 0.32 -0.42 -0.65 0.01
## tscore.2 0.44 0.78 0.34 0.10 -0.74 0.01
## tscore.10 0.14 0.45 0.31 0.54 1.06 0.01
## MI.3 0.15 0.36 0.22 0.29 -0.55 0.01
## MI.7 0.00 0.03 0.03 0.57 -0.71 0.00
## Logdicegt7 0.00 0.06 0.06 0.44 0.54 0.00
## DiversityMTLD 19.20 63.09 43.89 0.28 -0.68 1.61
## FrequencyJACETInfrequentwordratio 0.00 0.16 0.16 -0.19 -0.28 0.01
## WordCount 57.00 208.00 151.00 0.50 -0.65 6.28
## COCA_spoken_Range_Log_AW -0.52 -0.26 0.26 -0.46 0.63 0.01
## COCA_spoken_Frequency_Log_AW 2.92 3.36 0.44 -0.47 0.55 0.01
## COCA_spoken_Bigram_Frequency_Log 1.25 1.69 0.44 0.00 -0.96 0.02
## COCA_spoken_Bigram_Range_Log -1.51 -1.12 0.39 0.00 -0.81 0.02
## COCA_spoken_Trigram_Frequency_Log 0.25 0.87 0.62 -0.12 0.01 0.02
## COCA_spoken_Trigram_Range_Log -2.39 -1.82 0.57 -0.20 -0.06 0.02
## IndexCOCA_spoken_Frequency_Log_AW 1.41 1.91 0.50 0.23 -1.14 0.02
## FAC1_1 -1.88 2.04 3.92 0.02 -0.85 0.16
## FAC2_1 -2.66 2.28 4.95 -0.08 -0.14 0.16
## FAC3_1 -2.94 2.37 5.31 -0.63 0.85 0.16
## RawFirst 5.14 7.15 2.01 0.38 -0.82 0.09
## RawSecond 109.00 932.39 823.39 0.54 -1.03 36.79
## RawThird 90.48 1091.65 1001.17 1.62 3.30 33.88
## RawFourth 68.47 813.04 744.58 1.32 1.67 25.47
## T_First 1.93 17.04 15.11 0.28 -0.46 0.53
## T_Second 2.04 14.91 12.87 0.20 -0.42 0.48
## T_Third -0.73 12.22 12.95 -0.37 0.55 0.41
## T_Fourth -2.20 14.30 16.49 -0.40 0.35 0.51
## MI_First1 1.16 3.25 2.08 0.12 -0.47 0.08
## MI_Second 0.78 3.05 2.27 0.09 -0.35 0.08
## MI_Third 0.43 3.04 2.61 0.19 1.28 0.07
## MI_Fourth 0.34 2.51 2.17 -0.46 -0.72 0.09
## Richness 0.19 0.64 0.44 -0.11 -1.04 0.02
## MTLD 19.20 63.09 43.89 0.28 -0.68 1.61
## Fluency 0.24 0.83 0.59 0.07 -1.16 0.03
## ArticulationRate 50.95 176.20 125.25 0.14 -0.26 4.21
## FilledPause 0.00 0.22 0.22 0.89 -0.44 0.01
## SilentPause 0.28 1.16 0.88 0.51 -0.35 0.03
## invertedRawFreq -712.80 -200.70 512.10 -0.35 -0.85 20.44
## invertedFirstRawFreq -1278.52 -170.88 1107.64 -1.31 0.90 46.59Correlational analysis
Correlation between collocation knowledge measures
freq_tscore = rob.cor.mcmc(cbind(Rawfreq, tscore), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.6531716, SD = 0.09721351
## Posterior median and MAD: Median = 0.6645686, MAD = 0.09429324
## Rho values with 99% posterior probability: 99% HPDI = [0.368715, 0.8486897]
## Rho values with 95% posterior probability: 95% HPDI = [0.4548916, 0.8233276]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 1
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 6.25e-05
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.9995
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.986375
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.7328125print(freq_tscore)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 5.92 0.00 0.06 5.81 5.88 5.92 5.96 6.03 11532 1
## mu[2] 7.49 0.00 0.32 6.85 7.27 7.49 7.70 8.12 11764 1
## sigma[1] 0.34 0.00 0.04 0.27 0.31 0.34 0.37 0.43 11578 1
## sigma[2] 1.95 0.00 0.24 1.54 1.78 1.93 2.10 2.47 11505 1
## nu 27.95 0.11 14.91 8.16 17.11 24.80 35.60 64.27 18061 1
## rho 0.65 0.00 0.10 0.43 0.59 0.66 0.72 0.81 11318 1
## cov[1,1] 0.12 0.00 0.03 0.07 0.10 0.11 0.13 0.19 11223 1
## cov[1,2] 0.44 0.00 0.14 0.23 0.34 0.42 0.52 0.77 8569 1
## cov[2,1] 0.44 0.00 0.14 0.23 0.34 0.42 0.52 0.77 8569 1
## cov[2,2] 3.86 0.01 0.97 2.39 3.17 3.73 4.42 6.11 11185 1
## x_rand[1] 5.92 0.00 0.36 5.19 5.68 5.92 6.15 6.65 15468 1
## x_rand[2] 7.47 0.02 2.08 3.36 6.14 7.48 8.80 11.62 15662 1
## lp__ -38.81 0.02 1.76 -43.14 -39.73 -38.50 -37.53 -36.35 7449 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:46:22 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(freq_tscore, tscore, Rawfreq)
freq_MI = rob.cor.mcmc(cbind(Rawfreq, MI), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.3227581, SD = 0.1496301
## Posterior median and MAD: Median = 0.3300694, MAD = 0.1515278
## Rho values with 99% posterior probability: 99% HPDI = [-0.09185931, 0.6562387]
## Rho values with 95% posterior probability: 95% HPDI = [0.02322832, 0.6030461]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.0216875
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.9783125
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.07175
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.0315625
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.6970625
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.3196875
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0216875print(freq_MI)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 5.92 0.00 0.06 5.81 5.88 5.92 5.96 6.03 17074 1
## mu[2] 1.83 0.00 0.06 1.72 1.79 1.83 1.87 1.94 17326 1
## sigma[1] 0.34 0.00 0.04 0.27 0.31 0.34 0.37 0.44 16589 1
## sigma[2] 0.34 0.00 0.04 0.26 0.31 0.33 0.36 0.43 17332 1
## nu 26.53 0.11 14.82 7.22 15.66 23.43 33.89 63.42 19682 1
## rho 0.32 0.00 0.15 0.01 0.22 0.33 0.43 0.59 17947 1
## cov[1,1] 0.12 0.00 0.03 0.07 0.10 0.11 0.13 0.19 15814 1
## cov[1,2] 0.04 0.00 0.02 0.00 0.02 0.04 0.05 0.09 14196 1
## cov[2,1] 0.04 0.00 0.02 0.00 0.02 0.04 0.05 0.09 14196 1
## cov[2,2] 0.12 0.00 0.03 0.07 0.09 0.11 0.13 0.19 16287 1
## x_rand[1] 5.92 0.00 0.37 5.19 5.68 5.92 6.15 6.64 15820 1
## x_rand[2] 1.83 0.00 0.37 1.10 1.60 1.83 2.07 2.56 15140 1
## lp__ 20.37 0.02 1.77 16.12 19.45 20.70 21.66 22.81 7463 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:46:38 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(freq_MI, MI, Rawfreq)
tscore_MI = rob.cor.mcmc(cbind(tscore, MI), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.7891313, SD = 0.06433779
## Posterior median and MAD: Median = 0.7972896, MAD = 0.06065465
## Rho values with 99% posterior probability: 99% HPDI = [0.5907299, 0.9168299]
## Rho values with 95% posterior probability: 95% HPDI = [0.6576899, 0.9004247]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 1
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 1
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 1
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.9900625print(tscore_MI)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 7.49 0.00 0.32 6.86 7.28 7.49 7.70 8.12 8810 1
## mu[2] 1.83 0.00 0.05 1.72 1.79 1.83 1.86 1.94 8944 1
## sigma[1] 1.93 0.00 0.24 1.52 1.76 1.91 2.07 2.44 8692 1
## sigma[2] 0.33 0.00 0.04 0.26 0.30 0.33 0.36 0.42 8718 1
## nu 26.11 0.12 14.75 7.06 15.38 22.85 33.54 63.05 14827 1
## rho 0.79 0.00 0.06 0.64 0.75 0.80 0.84 0.89 10231 1
## cov[1,1] 3.76 0.01 0.94 2.31 3.10 3.63 4.28 5.96 8487 1
## cov[1,2] 0.51 0.00 0.14 0.29 0.41 0.49 0.59 0.85 7257 1
## cov[2,1] 0.51 0.00 0.14 0.29 0.41 0.49 0.59 0.85 7257 1
## cov[2,2] 0.11 0.00 0.03 0.07 0.09 0.11 0.13 0.18 8654 1
## x_rand[1] 7.47 0.02 2.09 3.36 6.13 7.48 8.82 11.62 15439 1
## x_rand[2] 1.83 0.00 0.36 1.11 1.60 1.83 2.06 2.53 16026 1
## lp__ -29.83 0.02 1.76 -34.12 -30.80 -29.50 -28.53 -27.38 6835 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:46:54 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(tscore_MI, MI, tscore)
Correlational analysis on Total response measures
Fluency rating (speech rate)
Fluency_RawFreq = rob.cor.mcmc(cbind(Fluency, Rawfreq), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.1291422, SD = 0.1605817
## Posterior median and MAD: Median = -0.131612, MAD = 0.1633996
## Rho values with 99% posterior probability: 99% HPDI = [-0.5223624, 0.2803069]
## Rho values with 95% posterior probability: 95% HPDI = [-0.4368925, 0.185007]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.7885
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.2115
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.343
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.170875
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.2428125
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.0424375
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 5e-04print(Fluency_RawFreq)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.52 0.00 0.03 0.46 0.50 0.52 0.54 0.58 19339 1
## mu[2] 5.92 0.00 0.06 5.81 5.89 5.93 5.96 6.04 20953 1
## sigma[1] 0.17 0.00 0.02 0.14 0.16 0.17 0.19 0.22 19044 1
## sigma[2] 0.35 0.00 0.04 0.27 0.32 0.34 0.37 0.44 16911 1
## nu 29.25 0.10 15.07 9.01 18.29 26.21 36.85 66.50 21371 1
## rho -0.13 0.00 0.16 -0.43 -0.24 -0.13 -0.02 0.19 19363 1
## cov[1,1] 0.03 0.00 0.01 0.02 0.02 0.03 0.03 0.05 17842 1
## cov[1,2] -0.01 0.00 0.01 -0.03 -0.01 -0.01 0.00 0.01 15475 1
## cov[2,1] -0.01 0.00 0.01 -0.03 -0.01 -0.01 0.00 0.01 15475 1
## cov[2,2] 0.12 0.00 0.03 0.07 0.10 0.12 0.14 0.19 15459 1
## x_rand[1] 0.52 0.00 0.19 0.16 0.40 0.52 0.64 0.89 15994 1
## x_rand[2] 5.93 0.00 0.37 5.19 5.69 5.93 6.16 6.66 16004 1
## lp__ 45.14 0.02 1.77 40.88 44.20 45.47 46.43 47.55 7650 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:47:07 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(Fluency_RawFreq, Rawfreq, Fluency)
Fluency_tscore = rob.cor.mcmc(cbind(Fluency, tscore), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.09449891, SD = 0.1618102
## Posterior median and MAD: Median = -0.09772779, MAD = 0.1648836
## Rho values with 99% posterior probability: 99% HPDI = [-0.5091974, 0.301825]
## Rho values with 95% posterior probability: 95% HPDI = [-0.4049108, 0.2224573]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.718125
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.281875
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.3866875
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.1983125
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.191625
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.0265625
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.000125print(Fluency_tscore)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.52 0.00 0.03 0.46 0.50 0.52 0.54 0.57 20013 1
## mu[2] 7.48 0.00 0.32 6.84 7.26 7.48 7.69 8.11 18914 1
## sigma[1] 0.17 0.00 0.02 0.14 0.16 0.17 0.19 0.22 18159 1
## sigma[2] 1.96 0.00 0.25 1.53 1.78 1.94 2.11 2.51 17674 1
## nu 27.71 0.10 14.82 8.04 16.97 24.69 35.14 65.20 21894 1
## rho -0.09 0.00 0.16 -0.40 -0.21 -0.10 0.02 0.23 17678 1
## cov[1,1] 0.03 0.00 0.01 0.02 0.02 0.03 0.03 0.05 17024 1
## cov[1,2] -0.03 0.00 0.06 -0.16 -0.07 -0.03 0.01 0.08 14105 1
## cov[2,1] -0.03 0.00 0.06 -0.16 -0.07 -0.03 0.01 0.08 14105 1
## cov[2,2] 3.90 0.01 1.03 2.34 3.18 3.75 4.44 6.31 16431 1
## x_rand[1] 0.52 0.00 0.19 0.15 0.40 0.52 0.64 0.88 15949 1
## x_rand[2] 7.49 0.02 2.09 3.39 6.14 7.50 8.84 11.62 15643 1
## lp__ -23.00 0.02 1.78 -27.38 -23.95 -22.65 -21.68 -20.56 7105 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:47:18 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(Fluency_tscore, tscore, Fluency)
Fluency_MI = rob.cor.mcmc(cbind(Fluency, MI), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.08546026, SD = 0.1631664
## Posterior median and MAD: Median = 0.08865775, MAD = 0.1652713
## Rho values with 99% posterior probability: 99% HPDI = [-0.3349234, 0.4725509]
## Rho values with 95% posterior probability: 95% HPDI = [-0.2305266, 0.3998928]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.2994375
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.7005625
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.391875
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.206875
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.183375
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.022625
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0001875print(Fluency_MI)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.52 0.00 0.03 0.46 0.50 0.52 0.54 0.58 19712 1
## mu[2] 1.82 0.00 0.06 1.71 1.79 1.82 1.86 1.93 19224 1
## sigma[1] 0.17 0.00 0.02 0.14 0.16 0.17 0.18 0.22 17919 1
## sigma[2] 0.34 0.00 0.04 0.26 0.31 0.33 0.36 0.43 19153 1
## nu 27.14 0.10 14.62 7.62 16.43 24.18 34.72 63.39 20759 1
## rho 0.09 0.00 0.16 -0.24 -0.02 0.09 0.20 0.39 17671 1
## cov[1,1] 0.03 0.00 0.01 0.02 0.02 0.03 0.03 0.05 16610 1
## cov[1,2] 0.01 0.00 0.01 -0.02 0.00 0.00 0.01 0.03 14351 1
## cov[2,1] 0.01 0.00 0.01 -0.02 0.00 0.00 0.01 0.03 14351 1
## cov[2,2] 0.12 0.00 0.03 0.07 0.09 0.11 0.13 0.19 18262 1
## x_rand[1] 0.52 0.00 0.18 0.15 0.40 0.52 0.64 0.89 15801 1
## x_rand[2] 1.82 0.00 0.36 1.11 1.60 1.82 2.05 2.55 16122 1
## lp__ 45.37 0.02 1.76 41.04 44.43 45.70 46.66 47.81 7524 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:47:29 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(Fluency_MI, MI, Fluency)
Articulation Rate
ArticulationRate_RawFreq = rob.cor.mcmc(cbind(ArticulationRate, Rawfreq), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.0566811, SD = 0.163747
## Posterior median and MAD: Median = -0.05736719, MAD = 0.1684909
## Rho values with 99% posterior probability: 99% HPDI = [-0.4487793, 0.3658917]
## Rho values with 95% posterior probability: 95% HPDI = [-0.36673, 0.2657182]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.6335
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.3665
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.4251875
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.21975
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.15525
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.01625
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0001875print(ArticulationRate_RawFreq)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
## mu[1] 109.01 0.03 4.46 100.34 106.05 109.01 111.98 117.83 19402
## mu[2] 5.92 0.00 0.06 5.81 5.88 5.92 5.96 6.03 19364
## sigma[1] 26.93 0.03 3.43 21.06 24.52 26.62 29.02 34.48 18431
## sigma[2] 0.35 0.00 0.04 0.27 0.32 0.34 0.37 0.44 18747
## nu 27.64 0.10 14.85 8.00 16.73 24.54 35.27 64.40 21587
## rho -0.06 0.00 0.16 -0.37 -0.17 -0.06 0.06 0.27 18464
## cov[1,1] 736.89 1.45 191.96 443.63 601.14 708.72 842.40 1188.60 17623
## cov[1,2] -0.54 0.01 1.64 -3.86 -1.55 -0.50 0.50 2.68 15234
## cov[2,1] -0.54 0.01 1.64 -3.86 -1.55 -0.50 0.50 2.68 15234
## cov[2,2] 0.12 0.00 0.03 0.07 0.10 0.12 0.14 0.20 17491
## x_rand[1] 108.94 0.23 28.90 51.07 90.30 109.16 127.75 165.45 16093
## x_rand[2] 5.92 0.00 0.37 5.18 5.68 5.92 6.16 6.64 16266
## lp__ -152.63 0.02 1.79 -157.03 -153.57 -152.30 -151.32 -150.19 7226
## Rhat
## mu[1] 1
## mu[2] 1
## sigma[1] 1
## sigma[2] 1
## nu 1
## rho 1
## cov[1,1] 1
## cov[1,2] 1
## cov[2,1] 1
## cov[2,2] 1
## x_rand[1] 1
## x_rand[2] 1
## lp__ 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:47:41 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(ArticulationRate_RawFreq, Rawfreq, ArticulationRate)
ArticulationRate_tscore = rob.cor.mcmc(cbind(ArticulationRate, tscore), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.01932372, SD = 0.1621637
## Posterior median and MAD: Median = 0.02062794, MAD = 0.1656464
## Rho values with 99% posterior probability: 99% HPDI = [-0.3964707, 0.4159959]
## Rho values with 95% posterior probability: 95% HPDI = [-0.3064207, 0.3215319]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.448875
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.551125
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.446625
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.234875
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.1275625
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.012
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0print(ArticulationRate_tscore)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
## mu[1] 108.74 0.03 4.43 99.86 105.85 108.76 111.68 117.44 19968
## mu[2] 7.48 0.00 0.33 6.83 7.26 7.48 7.69 8.11 21227
## sigma[1] 26.87 0.02 3.48 20.96 24.44 26.57 28.98 34.46 20411
## sigma[2] 1.96 0.00 0.25 1.53 1.78 1.94 2.11 2.50 19638
## nu 26.00 0.10 14.48 7.13 15.50 22.90 33.29 62.40 21202
## rho 0.02 0.00 0.16 -0.30 -0.09 0.02 0.13 0.33 19967
## cov[1,1] 734.16 1.40 194.78 439.23 597.53 706.10 840.05 1187.69 19232
## cov[1,2] 1.06 0.07 9.16 -17.26 -4.57 1.01 6.74 19.37 16362
## cov[2,1] 1.06 0.07 9.16 -17.26 -4.57 1.01 6.74 19.37 16362
## cov[2,2] 3.90 0.01 1.01 2.36 3.19 3.75 4.45 6.26 18130
## x_rand[1] 108.33 0.23 29.08 50.36 89.71 108.28 126.85 166.20 15785
## x_rand[2] 7.47 0.02 2.12 3.24 6.11 7.46 8.82 11.68 15883
## lp__ -220.65 0.02 1.78 -224.95 -221.59 -220.31 -219.35 -218.21 7256
## Rhat
## mu[1] 1
## mu[2] 1
## sigma[1] 1
## sigma[2] 1
## nu 1
## rho 1
## cov[1,1] 1
## cov[1,2] 1
## cov[2,1] 1
## cov[2,2] 1
## x_rand[1] 1
## x_rand[2] 1
## lp__ 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:47:54 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(ArticulationRate_tscore, tscore, ArticulationRate)
ArticulationRate_MI = rob.cor.mcmc(cbind(ArticulationRate, MI), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.1420418, SD = 0.1622194
## Posterior median and MAD: Median = 0.1456006, MAD = 0.1620058
## Rho values with 99% posterior probability: 99% HPDI = [-0.2782159, 0.5273764]
## Rho values with 95% posterior probability: 95% HPDI = [-0.1733782, 0.45813]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.1905
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.8095
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.3169375
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.1559375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.2691875
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.054875
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 5e-04print(ArticulationRate_MI)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
## mu[1] 109.03 0.03 4.46 100.27 106.01 109.07 112.01 117.77 22174
## mu[2] 1.82 0.00 0.06 1.71 1.79 1.82 1.86 1.93 20274
## sigma[1] 26.81 0.03 3.43 20.88 24.43 26.51 28.88 34.48 17741
## sigma[2] 0.34 0.00 0.04 0.26 0.31 0.33 0.36 0.44 19487
## nu 25.45 0.10 14.46 6.85 14.92 22.34 32.70 61.45 21151
## rho 0.14 0.00 0.16 -0.19 0.04 0.15 0.25 0.45 19938
## cov[1,1] 730.53 1.47 190.79 436.08 596.70 702.62 833.83 1189.16 16924
## cov[1,2] 1.32 0.01 1.63 -1.78 0.30 1.24 2.26 4.72 15459
## cov[2,1] 1.32 0.01 1.63 -1.78 0.30 1.24 2.26 4.72 15459
## cov[2,2] 0.12 0.00 0.03 0.07 0.10 0.11 0.13 0.19 18187
## x_rand[1] 109.30 0.23 29.23 50.97 90.59 109.22 128.04 167.56 15722
## x_rand[2] 1.82 0.00 0.36 1.10 1.59 1.82 2.05 2.54 15386
## lp__ -151.89 0.02 1.80 -156.31 -152.84 -151.57 -150.57 -149.41 6096
## Rhat
## mu[1] 1
## mu[2] 1
## sigma[1] 1
## sigma[2] 1
## nu 1
## rho 1
## cov[1,1] 1
## cov[1,2] 1
## cov[2,1] 1
## cov[2,2] 1
## x_rand[1] 1
## x_rand[2] 1
## lp__ 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:48:07 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(ArticulationRate_MI, MI, ArticulationRate)
Silent Pause ratio
SilentPause_RawFreq = rob.cor.mcmc(cbind(SilentPause, Rawfreq), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.147073, SD = 0.1621543
## Posterior median and MAD: Median = 0.1497355, MAD = 0.1656522
## Rho values with 99% posterior probability: 99% HPDI = [-0.2588787, 0.5319099]
## Rho values with 95% posterior probability: 95% HPDI = [-0.1560767, 0.4704009]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.1866875
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.8133125
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.314375
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.15825
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.2801875
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.0559375
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.001125print(SilentPause_RawFreq)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.59 0.00 0.04 0.53 0.57 0.59 0.62 0.66 19662 1
## mu[2] 5.92 0.00 0.06 5.81 5.89 5.92 5.96 6.04 20221 1
## sigma[1] 0.21 0.00 0.03 0.17 0.19 0.21 0.23 0.27 18561 1
## sigma[2] 0.34 0.00 0.04 0.27 0.31 0.34 0.37 0.44 18666 1
## nu 27.09 0.10 14.57 7.76 16.60 24.05 34.21 62.93 21738 1
## rho 0.15 0.00 0.16 -0.18 0.04 0.15 0.26 0.45 20786 1
## cov[1,1] 0.05 0.00 0.01 0.03 0.04 0.04 0.05 0.08 17256 1
## cov[1,2] 0.01 0.00 0.01 -0.01 0.00 0.01 0.02 0.04 16899 1
## cov[2,1] 0.01 0.00 0.01 -0.01 0.00 0.01 0.02 0.04 16899 1
## cov[2,2] 0.12 0.00 0.03 0.07 0.10 0.12 0.14 0.19 17478 1
## x_rand[1] 0.60 0.00 0.23 0.15 0.45 0.60 0.74 1.05 15521 1
## x_rand[2] 5.93 0.00 0.37 5.19 5.69 5.92 6.16 6.67 16150 1
## lp__ 36.37 0.02 1.80 31.97 35.43 36.71 37.68 38.83 6780 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:48:18 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(SilentPause_RawFreq, Rawfreq, SilentPause)
SilentPause_tscore = rob.cor.mcmc(cbind(SilentPause, tscore), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.09399211, SD = 0.161006
## Posterior median and MAD: Median = 0.0958358, MAD = 0.162334
## Rho values with 99% posterior probability: 99% HPDI = [-0.3087875, 0.4999733]
## Rho values with 95% posterior probability: 95% HPDI = [-0.2286147, 0.4017997]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.2794375
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.7205625
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.390625
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.200375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.18375
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.02775
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0003125print(SilentPause_tscore)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.60 0.00 0.04 0.53 0.57 0.60 0.62 0.67 19496 1
## mu[2] 7.48 0.00 0.32 6.85 7.27 7.48 7.70 8.13 18197 1
## sigma[1] 0.21 0.00 0.03 0.17 0.20 0.21 0.23 0.28 17023 1
## sigma[2] 1.96 0.00 0.25 1.54 1.79 1.94 2.12 2.52 17735 1
## nu 26.87 0.10 14.72 7.62 16.09 23.64 34.53 63.05 20069 1
## rho 0.09 0.00 0.16 -0.23 -0.01 0.10 0.21 0.40 16842 1
## cov[1,1] 0.05 0.00 0.01 0.03 0.04 0.04 0.05 0.08 16068 1
## cov[1,2] 0.04 0.00 0.07 -0.10 -0.01 0.04 0.09 0.20 13928 1
## cov[2,1] 0.04 0.00 0.07 -0.10 -0.01 0.04 0.09 0.20 13928 1
## cov[2,2] 3.92 0.01 1.02 2.37 3.19 3.76 4.47 6.35 16559 1
## x_rand[1] 0.60 0.00 0.23 0.13 0.45 0.60 0.74 1.06 16109 1
## x_rand[2] 7.48 0.02 2.09 3.32 6.15 7.50 8.83 11.62 16034 1
## lp__ -31.95 0.02 1.79 -36.30 -32.91 -31.61 -30.62 -29.49 7562 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:48:29 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(SilentPause_tscore, tscore, SilentPause)
SilentPause_MI = rob.cor.mcmc(cbind(SilentPause, MI), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.01559714, SD = 0.165624
## Posterior median and MAD: Median = 0.01651298, MAD = 0.1665637
## Rho values with 99% posterior probability: 99% HPDI = [-0.4152384, 0.4319221]
## Rho values with 95% posterior probability: 95% HPDI = [-0.3132122, 0.3331659]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.462875
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.537125
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.4506875
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.2324375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.135875
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.01575
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0001875print(SilentPause_MI)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.59 0.00 0.03 0.53 0.57 0.59 0.62 0.66 21625 1
## mu[2] 1.82 0.00 0.06 1.71 1.79 1.82 1.86 1.93 23504 1
## sigma[1] 0.21 0.00 0.03 0.16 0.19 0.21 0.23 0.27 19376 1
## sigma[2] 0.34 0.00 0.04 0.26 0.31 0.33 0.36 0.43 19070 1
## nu 24.39 0.10 14.16 6.23 14.06 21.37 31.38 59.96 21045 1
## rho 0.02 0.00 0.17 -0.31 -0.10 0.02 0.13 0.34 20634 1
## cov[1,1] 0.05 0.00 0.01 0.03 0.04 0.04 0.05 0.07 18126 1
## cov[1,2] 0.00 0.00 0.01 -0.02 -0.01 0.00 0.01 0.03 16359 1
## cov[2,1] 0.00 0.00 0.01 -0.02 -0.01 0.00 0.01 0.03 16359 1
## cov[2,2] 0.11 0.00 0.03 0.07 0.09 0.11 0.13 0.18 18023 1
## x_rand[1] 0.60 0.00 0.23 0.14 0.45 0.59 0.74 1.05 16097 1
## x_rand[2] 1.82 0.00 0.36 1.11 1.59 1.82 2.05 2.55 16116 1
## lp__ 36.48 0.02 1.78 32.16 35.53 36.80 37.79 38.93 6802 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:48:40 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(SilentPause_MI, MI, SilentPause)
Filled pause ratio
FilledPause_RawFreq = rob.cor.mcmc(cbind(FilledPause, Rawfreq), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.3254999, SD = 0.1560133
## Posterior median and MAD: Median = -0.3326866, MAD = 0.1559201
## Rho values with 99% posterior probability: 99% HPDI = [-0.680629, 0.1036161]
## Rho values with 95% posterior probability: 95% HPDI = [-0.6327542, -0.02885761]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.9748125
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.0251875
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.07475
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.0325
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.6996875
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.3305
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0283125print(FilledPause_RawFreq)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.07 0.00 0.01 0.05 0.06 0.07 0.07 0.09 16004 1
## mu[2] 5.93 0.00 0.06 5.81 5.89 5.93 5.96 6.04 16908 1
## sigma[1] 0.06 0.00 0.01 0.05 0.05 0.06 0.06 0.08 15967 1
## sigma[2] 0.34 0.00 0.04 0.27 0.31 0.34 0.37 0.44 16632 1
## nu 22.35 0.10 13.82 5.27 12.28 19.11 29.14 57.53 18424 1
## rho -0.33 0.00 0.16 -0.61 -0.44 -0.33 -0.22 0.00 17737 1
## cov[1,1] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 15572 1
## cov[1,2] -0.01 0.00 0.00 -0.02 -0.01 -0.01 0.00 0.00 13741 1
## cov[2,1] -0.01 0.00 0.00 -0.02 -0.01 -0.01 0.00 0.00 13741 1
## cov[2,2] 0.12 0.00 0.03 0.07 0.10 0.11 0.13 0.19 15927 1
## x_rand[1] 0.07 0.00 0.07 -0.06 0.03 0.07 0.11 0.20 15851 1
## x_rand[2] 5.93 0.00 0.38 5.18 5.69 5.93 6.16 6.68 15835 1
## lp__ 86.86 0.02 1.77 82.58 85.92 87.20 88.16 89.31 7261 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:48:52 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(FilledPause_RawFreq, Rawfreq, FilledPause)
FilledPause_tscore = rob.cor.mcmc(cbind(FilledPause, tscore), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.2819368, SD = 0.1518944
## Posterior median and MAD: Median = -0.2884884, MAD = 0.1537399
## Rho values with 99% posterior probability: 99% HPDI = [-0.6306421, 0.1248719]
## Rho values with 95% posterior probability: 95% HPDI = [-0.5737772, 0.01302256]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.96025
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.03975
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.113875
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.054375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.5998125
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.2294375
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0091875print(FilledPause_tscore)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.07 0.00 0.01 0.05 0.06 0.07 0.08 0.09 15902 1
## mu[2] 7.52 0.00 0.33 6.88 7.30 7.52 7.74 8.17 17822 1
## sigma[1] 0.06 0.00 0.01 0.05 0.06 0.06 0.07 0.08 16588 1
## sigma[2] 1.94 0.00 0.25 1.52 1.77 1.92 2.09 2.50 17555 1
## nu 25.21 0.11 14.54 6.43 14.59 22.04 32.68 61.38 19026 1
## rho -0.28 0.00 0.15 -0.56 -0.39 -0.29 -0.18 0.03 17314 1
## cov[1,1] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 15658 1
## cov[1,2] -0.03 0.00 0.02 -0.08 -0.05 -0.03 -0.02 0.00 14650 1
## cov[2,1] -0.03 0.00 0.02 -0.08 -0.05 -0.03 -0.02 0.00 14650 1
## cov[2,2] 3.84 0.01 1.00 2.30 3.14 3.70 4.39 6.25 16578 1
## x_rand[1] 0.07 0.00 0.07 -0.06 0.03 0.07 0.11 0.20 15815 1
## x_rand[2] 7.53 0.02 2.10 3.35 6.19 7.55 8.88 11.67 15153 1
## lp__ 18.09 0.02 1.79 13.79 17.14 18.43 19.41 20.57 7204 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:49:05 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(FilledPause_tscore, tscore, FilledPause)
FilledPause_MI = rob.cor.mcmc(cbind(FilledPause, MI), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.121326, SD = 0.1609757
## Posterior median and MAD: Median = -0.1249063, MAD = 0.1632253
## Rho values with 99% posterior probability: 99% HPDI = [-0.5025058, 0.2985371]
## Rho values with 95% posterior probability: 95% HPDI = [-0.4418612, 0.1798861]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.7746875
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.2253125
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.350875
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.1751875
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.230875
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.0386875
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0005625print(FilledPause_MI)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.07 0.00 0.01 0.05 0.06 0.07 0.08 0.09 20815 1
## mu[2] 1.83 0.00 0.06 1.71 1.79 1.83 1.86 1.94 20411 1
## sigma[1] 0.06 0.00 0.01 0.05 0.06 0.06 0.07 0.08 17743 1
## sigma[2] 0.34 0.00 0.04 0.26 0.31 0.33 0.36 0.43 18631 1
## nu 25.34 0.10 14.66 6.40 14.67 22.15 32.70 61.91 20283 1
## rho -0.12 0.00 0.16 -0.43 -0.23 -0.12 -0.01 0.21 20049 1
## cov[1,1] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 17162 1
## cov[1,2] 0.00 0.00 0.00 -0.01 0.00 0.00 0.00 0.00 16596 1
## cov[2,1] 0.00 0.00 0.00 -0.01 0.00 0.00 0.00 0.00 16596 1
## cov[2,2] 0.12 0.00 0.03 0.07 0.09 0.11 0.13 0.19 17715 1
## x_rand[1] 0.07 0.00 0.07 -0.06 0.03 0.07 0.11 0.20 16190 1
## x_rand[2] 1.83 0.00 0.37 1.10 1.60 1.83 2.06 2.55 16219 1
## lp__ 85.22 0.02 1.77 80.87 84.26 85.54 86.52 87.67 6868 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:49:17 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(FilledPause_MI, MI, FilledPause)
Lexis
Richness rating
Richness_RawFreq = rob.cor.mcmc(cbind(Richness, Rawfreq), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.1773432, SD = 0.159801
## Posterior median and MAD: Median = -0.1815353, MAD = 0.1629681
## Rho values with 99% posterior probability: 99% HPDI = [-0.5768741, 0.22718]
## Rho values with 95% posterior probability: 95% HPDI = [-0.4803125, 0.1355636]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.862375
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.137625
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.26675
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.132125
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.3406875
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.077625
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0016875print(Richness_RawFreq)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.42 0.00 0.02 0.38 0.40 0.42 0.43 0.46 18164 1
## mu[2] 5.93 0.00 0.06 5.81 5.89 5.93 5.96 6.04 19969 1
## sigma[1] 0.13 0.00 0.02 0.10 0.12 0.13 0.14 0.16 18318 1
## sigma[2] 0.35 0.00 0.04 0.27 0.32 0.34 0.37 0.44 20251 1
## nu 29.52 0.10 15.32 8.98 18.39 26.48 37.38 67.45 21739 1
## rho -0.18 0.00 0.16 -0.48 -0.29 -0.18 -0.07 0.14 18185 1
## cov[1,1] 0.02 0.00 0.00 0.01 0.01 0.02 0.02 0.03 17240 1
## cov[1,2] -0.01 0.00 0.01 -0.03 -0.01 -0.01 0.00 0.01 14980 1
## cov[2,1] -0.01 0.00 0.01 -0.03 -0.01 -0.01 0.00 0.01 14980 1
## cov[2,2] 0.12 0.00 0.03 0.07 0.10 0.12 0.14 0.19 18949 1
## x_rand[1] 0.42 0.00 0.14 0.15 0.33 0.42 0.50 0.69 16068 1
## x_rand[2] 5.93 0.00 0.37 5.19 5.69 5.93 6.16 6.64 16235 1
## lp__ 57.47 0.02 1.79 53.05 56.52 57.80 58.78 59.94 7489 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:49:28 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(Richness_RawFreq, Rawfreq, Richness)
Richness_tscore = rob.cor.mcmc(cbind(Richness, tscore), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.03770546, SD = 0.164284
## Posterior median and MAD: Median = -0.0379153, MAD = 0.1680372
## Rho values with 99% posterior probability: 99% HPDI = [-0.4439338, 0.3782282]
## Rho values with 95% posterior probability: 95% HPDI = [-0.3642209, 0.2739932]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.5898125
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.4101875
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.4390625
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.228875
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.1385
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.01625
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 6.25e-05print(Richness_tscore)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.42 0.00 0.02 0.38 0.40 0.42 0.43 0.46 18902 1
## mu[2] 7.49 0.00 0.32 6.85 7.27 7.49 7.70 8.11 20029 1
## sigma[1] 0.13 0.00 0.02 0.10 0.12 0.12 0.14 0.16 18116 1
## sigma[2] 1.96 0.00 0.25 1.54 1.79 1.94 2.11 2.52 18753 1
## nu 28.24 0.10 15.15 8.16 17.21 25.11 36.02 65.76 21564 1
## rho -0.04 0.00 0.16 -0.35 -0.15 -0.04 0.07 0.29 18947 1
## cov[1,1] 0.02 0.00 0.00 0.01 0.01 0.02 0.02 0.03 17063 1
## cov[1,2] -0.01 0.00 0.04 -0.10 -0.04 -0.01 0.02 0.08 15297 1
## cov[2,1] -0.01 0.00 0.04 -0.10 -0.04 -0.01 0.02 0.08 15297 1
## cov[2,2] 3.91 0.01 1.00 2.38 3.21 3.77 4.44 6.33 17708 1
## x_rand[1] 0.42 0.00 0.14 0.14 0.33 0.42 0.50 0.68 15434 1
## x_rand[2] 7.50 0.02 2.10 3.28 6.19 7.50 8.84 11.66 16040 1
## lp__ -11.13 0.02 1.78 -15.46 -12.07 -10.78 -9.84 -8.68 7354 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:49:39 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(Richness_tscore, tscore, Richness)
Richness_MI = rob.cor.mcmc(cbind(Richness, MI), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.1399738, SD = 0.1607093
## Posterior median and MAD: Median = 0.1443422, MAD = 0.1639349
## Rho values with 99% posterior probability: 99% HPDI = [-0.266725, 0.5330212]
## Rho values with 95% posterior probability: 95% HPDI = [-0.1691515, 0.4522867]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.1949375
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.8050625
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.3230625
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.167
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.2634375
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.049125
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 5e-04print(Richness_MI)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.42 0.00 0.02 0.38 0.40 0.42 0.43 0.46 19492 1
## mu[2] 1.82 0.00 0.06 1.72 1.79 1.82 1.86 1.94 20313 1
## sigma[1] 0.13 0.00 0.02 0.10 0.11 0.12 0.14 0.16 18127 1
## sigma[2] 0.34 0.00 0.04 0.27 0.31 0.33 0.36 0.43 18912 1
## nu 27.03 0.10 14.55 7.61 16.40 24.14 34.21 63.17 20773 1
## rho 0.14 0.00 0.16 -0.18 0.03 0.14 0.25 0.44 18067 1
## cov[1,1] 0.02 0.00 0.00 0.01 0.01 0.02 0.02 0.03 17252 1
## cov[1,2] 0.01 0.00 0.01 -0.01 0.00 0.01 0.01 0.02 15278 1
## cov[2,1] 0.01 0.00 0.01 -0.01 0.00 0.01 0.01 0.02 15278 1
## cov[2,2] 0.12 0.00 0.03 0.07 0.10 0.11 0.13 0.19 17866 1
## x_rand[1] 0.41 0.00 0.13 0.15 0.33 0.41 0.50 0.68 15837 1
## x_rand[2] 1.82 0.00 0.36 1.10 1.59 1.82 2.05 2.54 15969 1
## lp__ 57.63 0.02 1.75 53.47 56.68 57.96 58.92 60.05 7910 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:49:50 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(Richness_MI, MI, Richness)
Diversity
MTLD_RawFreq = rob.cor.mcmc(cbind(MTLD, Rawfreq), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.2199496, SD = 0.155176
## Posterior median and MAD: Median = -0.2256312, MAD = 0.1571495
## Rho values with 99% posterior probability: 99% HPDI = [-0.5906061, 0.1832651]
## Rho values with 95% posterior probability: 95% HPDI = [-0.5212153, 0.08307372]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.91425
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.08575
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.1938125
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.09375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.438
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.121375
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.003print(MTLD_RawFreq)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
## mu[1] 37.02 0.01 1.72 33.64 35.89 37.04 38.14 40.42 20045
## mu[2] 5.93 0.00 0.06 5.81 5.89 5.93 5.96 6.04 19724
## sigma[1] 10.42 0.01 1.30 8.19 9.50 10.30 11.19 13.33 20648
## sigma[2] 0.35 0.00 0.04 0.27 0.32 0.34 0.37 0.44 18850
## nu 28.89 0.10 15.15 8.55 17.86 25.83 36.49 66.25 24952
## rho -0.22 0.00 0.16 -0.51 -0.33 -0.23 -0.12 0.10 20239
## cov[1,1] 110.24 0.20 28.25 67.10 90.30 106.11 125.32 177.74 19227
## cov[1,2] -0.81 0.01 0.64 -2.22 -1.18 -0.77 -0.39 0.35 16529
## cov[2,1] -0.81 0.01 0.64 -2.22 -1.18 -0.77 -0.39 0.35 16529
## cov[2,2] 0.12 0.00 0.03 0.07 0.10 0.12 0.14 0.19 17834
## x_rand[1] 37.02 0.09 11.10 15.03 29.85 36.97 44.10 58.99 15776
## x_rand[2] 5.93 0.00 0.37 5.19 5.69 5.93 6.17 6.67 16297
## lp__ -114.36 0.02 1.81 -118.62 -115.31 -114.02 -113.05 -111.88 6781
## Rhat
## mu[1] 1
## mu[2] 1
## sigma[1] 1
## sigma[2] 1
## nu 1
## rho 1
## cov[1,1] 1
## cov[1,2] 1
## cov[2,1] 1
## cov[2,2] 1
## x_rand[1] 1
## x_rand[2] 1
## lp__ 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:50:01 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(MTLD_RawFreq, Rawfreq, MTLD)
MTLD_tscore = rob.cor.mcmc(cbind(MTLD, tscore), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.1101038, SD = 0.1622575
## Posterior median and MAD: Median = -0.1144983, MAD = 0.1646903
## Rho values with 99% posterior probability: 99% HPDI = [-0.5139658, 0.2898092]
## Rho values with 95% posterior probability: 95% HPDI = [-0.4200336, 0.206725]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.7510625
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.2489375
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.362125
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.1853125
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.2128125
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.0344375
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 6.25e-05print(MTLD_tscore)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
## mu[1] 36.81 0.01 1.72 33.38 35.67 36.82 37.94 40.20 20889
## mu[2] 7.51 0.00 0.32 6.87 7.29 7.51 7.72 8.14 20542
## sigma[1] 10.34 0.01 1.31 8.13 9.42 10.22 11.13 13.27 19132
## sigma[2] 1.94 0.00 0.24 1.52 1.77 1.92 2.09 2.48 19573
## nu 25.83 0.10 14.20 7.19 15.43 23.03 33.00 61.29 21385
## rho -0.11 0.00 0.16 -0.42 -0.22 -0.11 0.00 0.21 20676
## cov[1,1] 108.72 0.21 28.30 66.12 88.81 104.48 123.89 176.13 18122
## cov[1,2] -2.28 0.03 3.56 -9.80 -4.44 -2.17 -0.01 4.37 16598
## cov[2,1] -2.28 0.03 3.56 -9.80 -4.44 -2.17 -0.01 4.37 16598
## cov[2,2] 3.82 0.01 0.98 2.30 3.13 3.67 4.36 6.14 18626
## x_rand[1] 37.01 0.09 11.12 14.76 29.94 37.07 44.15 58.76 15963
## x_rand[2] 7.50 0.02 2.07 3.34 6.18 7.52 8.82 11.59 15286
## lp__ -182.86 0.02 1.74 -187.13 -183.81 -182.53 -181.58 -180.44 7481
## Rhat
## mu[1] 1
## mu[2] 1
## sigma[1] 1
## sigma[2] 1
## nu 1
## rho 1
## cov[1,1] 1
## cov[1,2] 1
## cov[2,1] 1
## cov[2,2] 1
## x_rand[1] 1
## x_rand[2] 1
## lp__ 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:50:12 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(MTLD_tscore, tscore, MTLD)
MTLD_MI = rob.cor.mcmc(cbind(MTLD, MI), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.06902181, SD = 0.1640945
## Posterior median and MAD: Median = 0.07151461, MAD = 0.1664949
## Rho values with 99% posterior probability: 99% HPDI = [-0.3468243, 0.463558]
## Rho values with 95% posterior probability: 95% HPDI = [-0.2549611, 0.3830818]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.33625
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.66375
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.4133125
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.217375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.1635625
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.020875
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0001875print(MTLD_MI)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
## mu[1] 36.93 0.01 1.72 33.51 35.78 36.94 38.10 40.34 20702
## mu[2] 1.83 0.00 0.06 1.71 1.79 1.83 1.86 1.94 21094
## sigma[1] 10.39 0.01 1.30 8.16 9.48 10.28 11.21 13.19 19971
## sigma[2] 0.34 0.00 0.04 0.27 0.31 0.34 0.37 0.44 19566
## nu 26.90 0.10 14.78 7.60 16.01 23.78 34.32 63.96 21429
## rho 0.07 0.00 0.16 -0.25 -0.04 0.07 0.18 0.39 20962
## cov[1,1] 109.73 0.20 27.99 66.66 89.90 105.58 125.67 174.02 18896
## cov[1,2] 0.25 0.00 0.63 -0.98 -0.14 0.24 0.62 1.54 17367
## cov[2,1] 0.25 0.00 0.63 -0.98 -0.14 0.24 0.62 1.54 17367
## cov[2,2] 0.12 0.00 0.03 0.07 0.10 0.11 0.13 0.19 18191
## x_rand[1] 36.99 0.09 11.30 14.47 29.75 36.90 44.18 59.33 16067
## x_rand[2] 1.83 0.00 0.37 1.11 1.60 1.83 2.06 2.57 16155
## lp__ -115.04 0.02 1.79 -119.40 -116.02 -114.70 -113.72 -112.57 7486
## Rhat
## mu[1] 1
## mu[2] 1
## sigma[1] 1
## sigma[2] 1
## nu 1
## rho 1
## cov[1,1] 1
## cov[1,2] 1
## cov[2,1] 1
## cov[2,2] 1
## x_rand[1] 1
## x_rand[2] 1
## lp__ 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:50:23 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(MTLD_MI, MI, MTLD)
Frequency
COCA_spoken_Frequency_Log_AW_RawFreq = rob.cor.mcmc(cbind(COCA_spoken_Frequency_Log_AW, Rawfreq), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.007302924, SD = 0.1641856
## Posterior median and MAD: Median = -0.00761488, MAD = 0.1679714
## Rho values with 99% posterior probability: 99% HPDI = [-0.4018594, 0.4156321]
## Rho values with 95% posterior probability: 95% HPDI = [-0.324452, 0.312316]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.5209375
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.4790625
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.4515
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.2334375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.1301875
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.012375
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 6.25e-05print(COCA_spoken_Frequency_Log_AW_RawFreq)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 3.17 0.00 0.01 3.14 3.16 3.17 3.17 3.19 20014 1
## mu[2] 5.92 0.00 0.06 5.80 5.88 5.92 5.96 6.03 19582 1
## sigma[1] 0.08 0.00 0.01 0.06 0.08 0.08 0.09 0.11 18208 1
## sigma[2] 0.34 0.00 0.04 0.27 0.31 0.34 0.37 0.44 18764 1
## nu 23.88 0.10 14.00 6.04 13.69 20.74 30.80 59.09 19261 1
## rho -0.01 0.00 0.16 -0.32 -0.12 -0.01 0.10 0.31 19457 1
## cov[1,1] 0.01 0.00 0.00 0.00 0.01 0.01 0.01 0.01 17691 1
## cov[1,2] 0.00 0.00 0.01 -0.01 0.00 0.00 0.00 0.01 16427 1
## cov[2,1] 0.00 0.00 0.01 -0.01 0.00 0.00 0.00 0.01 16427 1
## cov[2,2] 0.12 0.00 0.03 0.07 0.10 0.12 0.14 0.19 16976 1
## x_rand[1] 3.17 0.00 0.09 2.98 3.11 3.17 3.22 3.35 15865 1
## x_rand[2] 5.92 0.00 0.37 5.18 5.69 5.92 6.15 6.65 15664 1
## lp__ 71.25 0.02 1.77 66.98 70.29 71.58 72.55 73.70 7125 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:50:35 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(COCA_spoken_Frequency_Log_AW_RawFreq, Rawfreq, COCA_spoken_Frequency_Log_AW)
COCA_spoken_Frequency_Log_AW_tscore = rob.cor.mcmc(cbind(COCA_spoken_Frequency_Log_AW, tscore), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.08681079, SD = 0.1630215
## Posterior median and MAD: Median = -0.09007074, MAD = 0.1647332
## Rho values with 99% posterior probability: 99% HPDI = [-0.4790912, 0.3391191]
## Rho values with 95% posterior probability: 95% HPDI = [-0.398883, 0.2351174]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.7029375
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.2970625
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.3946875
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.205375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.18325
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.025125
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0001875print(COCA_spoken_Frequency_Log_AW_tscore)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 3.17 0.00 0.01 3.14 3.16 3.17 3.18 3.19 19214 1
## mu[2] 7.50 0.00 0.32 6.87 7.28 7.50 7.71 8.12 19243 1
## sigma[1] 0.08 0.00 0.01 0.07 0.08 0.08 0.09 0.11 18457 1
## sigma[2] 1.95 0.00 0.25 1.51 1.77 1.93 2.10 2.51 19243 1
## nu 23.07 0.10 13.78 5.92 13.09 19.88 29.56 58.68 20002 1
## rho -0.09 0.00 0.16 -0.40 -0.20 -0.09 0.02 0.24 18155 1
## cov[1,1] 0.01 0.00 0.00 0.00 0.01 0.01 0.01 0.01 17612 1
## cov[1,2] -0.01 0.00 0.03 -0.08 -0.03 -0.01 0.00 0.04 14791 1
## cov[2,1] -0.01 0.00 0.03 -0.08 -0.03 -0.01 0.00 0.04 14791 1
## cov[2,2] 3.85 0.01 1.03 2.29 3.12 3.71 4.42 6.28 18327 1
## x_rand[1] 3.17 0.00 0.09 2.98 3.11 3.17 3.22 3.35 16149 1
## x_rand[2] 7.51 0.02 2.11 3.31 6.18 7.50 8.85 11.70 16094 1
## lp__ 3.35 0.02 1.79 -1.02 2.41 3.69 4.67 5.79 7184 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:50:47 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(COCA_spoken_Frequency_Log_AW_tscore, tscore, COCA_spoken_Frequency_Log_AW)
COCA_spoken_Frequency_Log_AW_MI = rob.cor.mcmc(cbind(COCA_spoken_Frequency_Log_AW, MI), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.3387694, SD = 0.1460515
## Posterior median and MAD: Median = -0.3456793, MAD = 0.145145
## Rho values with 99% posterior probability: 99% HPDI = [-0.6695534, 0.06706539]
## Rho values with 95% posterior probability: 95% HPDI = [-0.6144263, -0.04786768]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.9838125
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.0161875
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.05825
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.024875
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.740125
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.355375
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.026875print(COCA_spoken_Frequency_Log_AW_MI)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 3.17 0.00 0.01 3.14 3.16 3.17 3.17 3.19 17372 1
## mu[2] 1.83 0.00 0.06 1.71 1.79 1.83 1.86 1.94 15757 1
## sigma[1] 0.08 0.00 0.01 0.06 0.08 0.08 0.09 0.11 16967 1
## sigma[2] 0.34 0.00 0.04 0.26 0.31 0.33 0.36 0.43 17503 1
## nu 22.08 0.10 13.50 5.42 12.25 18.95 28.48 56.59 20145 1
## rho -0.34 0.00 0.15 -0.60 -0.44 -0.35 -0.25 -0.03 17753 1
## cov[1,1] 0.01 0.00 0.00 0.00 0.01 0.01 0.01 0.01 16785 1
## cov[1,2] -0.01 0.00 0.01 -0.02 -0.01 -0.01 -0.01 0.00 13807 1
## cov[2,1] -0.01 0.00 0.01 -0.02 -0.01 -0.01 -0.01 0.00 13807 1
## cov[2,2] 0.11 0.00 0.03 0.07 0.09 0.11 0.13 0.19 16797 1
## x_rand[1] 3.16 0.00 0.09 2.98 3.11 3.17 3.22 3.35 15768 1
## x_rand[2] 1.83 0.00 0.37 1.10 1.60 1.83 2.06 2.56 16061 1
## lp__ 73.92 0.02 1.79 69.57 72.96 74.28 75.25 76.38 6936 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:50:58 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(COCA_spoken_Frequency_Log_AW_MI, MI, COCA_spoken_Frequency_Log_AW)
Range
COCA_spoken_Range_Log_AW_RawFreq = rob.cor.mcmc(cbind(COCA_spoken_Range_Log_AW, Rawfreq), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.0370603, SD = 0.1688143
## Posterior median and MAD: Median = -0.03702124, MAD = 0.1722548
## Rho values with 99% posterior probability: 99% HPDI = [-0.4557317, 0.3977934]
## Rho values with 95% posterior probability: 95% HPDI = [-0.3517097, 0.3061047]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.58625
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.41375
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.4313125
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.2234375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.149625
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.0190625
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.00025print(COCA_spoken_Range_Log_AW_RawFreq)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] -0.38 0.00 0.01 -0.40 -0.38 -0.38 -0.37 -0.36 20692 1
## mu[2] 5.92 0.00 0.06 5.80 5.88 5.92 5.96 6.03 19308 1
## sigma[1] 0.05 0.00 0.01 0.04 0.04 0.05 0.05 0.06 17584 1
## sigma[2] 0.34 0.00 0.04 0.27 0.31 0.34 0.37 0.44 17737 1
## nu 21.94 0.10 13.79 5.06 11.87 18.76 28.43 57.73 20476 1
## rho -0.04 0.00 0.17 -0.36 -0.15 -0.04 0.08 0.30 18742 1
## cov[1,1] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 17732 1
## cov[1,2] 0.00 0.00 0.00 -0.01 0.00 0.00 0.00 0.01 15761 1
## cov[2,1] 0.00 0.00 0.00 -0.01 0.00 0.00 0.00 0.01 15761 1
## cov[2,2] 0.12 0.00 0.03 0.07 0.10 0.11 0.13 0.19 16738 1
## x_rand[1] -0.38 0.00 0.05 -0.49 -0.41 -0.38 -0.35 -0.28 16227 1
## x_rand[2] 5.92 0.00 0.37 5.18 5.69 5.92 6.16 6.66 16041 1
## lp__ 92.66 0.02 1.80 88.28 91.70 92.99 93.97 95.16 7297 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:51:11 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(COCA_spoken_Range_Log_AW_RawFreq, Rawfreq, COCA_spoken_Range_Log_AW)
COCA_spoken_Range_Log_AW_tscore = rob.cor.mcmc(cbind(COCA_spoken_Range_Log_AW, tscore), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.09699968, SD = 0.1690204
## Posterior median and MAD: Median = -0.09967865, MAD = 0.1721868
## Rho values with 99% posterior probability: 99% HPDI = [-0.5318362, 0.3245279]
## Rho values with 95% posterior probability: 95% HPDI = [-0.4210897, 0.2335799]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.716125
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.283875
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.377125
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.1915
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.2065
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.0348125
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 5e-04print(COCA_spoken_Range_Log_AW_tscore)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] -0.38 0.00 0.01 -0.40 -0.38 -0.38 -0.37 -0.36 19649 1
## mu[2] 7.49 0.00 0.32 6.85 7.27 7.49 7.70 8.12 19895 1
## sigma[1] 0.05 0.00 0.01 0.04 0.04 0.05 0.05 0.06 16854 1
## sigma[2] 1.92 0.00 0.25 1.49 1.75 1.90 2.08 2.49 18100 1
## nu 20.60 0.10 13.49 4.56 10.80 17.22 27.05 55.10 18167 1
## rho -0.10 0.00 0.17 -0.42 -0.21 -0.10 0.02 0.24 18367 1
## cov[1,1] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 16534 1
## cov[1,2] -0.01 0.00 0.02 -0.04 -0.02 -0.01 0.00 0.02 16089 1
## cov[2,1] -0.01 0.00 0.02 -0.04 -0.02 -0.01 0.00 0.02 16089 1
## cov[2,2] 3.76 0.01 1.01 2.23 3.06 3.62 4.31 6.18 17138 1
## x_rand[1] -0.38 0.00 0.05 -0.48 -0.41 -0.38 -0.35 -0.27 15756 1
## x_rand[2] 7.50 0.02 2.10 3.27 6.18 7.49 8.82 11.62 16711 1
## lp__ 24.76 0.02 1.78 20.46 23.83 25.07 26.07 27.19 7016 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:51:24 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(COCA_spoken_Range_Log_AW_tscore, tscore, COCA_spoken_Range_Log_AW)
COCA_spoken_Range_Log_AW_MI = rob.cor.mcmc(cbind(COCA_spoken_Range_Log_AW, MI), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.3471224, SD = 0.1522736
## Posterior median and MAD: Median = -0.3552053, MAD = 0.152433
## Rho values with 99% posterior probability: 99% HPDI = [-0.7058717, 0.06425495]
## Rho values with 95% posterior probability: 95% HPDI = [-0.6390006, -0.05065239]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.9819375
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.0180625
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.05675
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.0248125
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.746
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.3831875
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0364375print(COCA_spoken_Range_Log_AW_MI)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] -0.38 0.00 0.01 -0.39 -0.38 -0.38 -0.37 -0.36 17192 1
## mu[2] 1.82 0.00 0.06 1.71 1.79 1.82 1.86 1.93 15498 1
## sigma[1] 0.05 0.00 0.01 0.03 0.04 0.05 0.05 0.06 14130 1
## sigma[2] 0.33 0.00 0.05 0.25 0.30 0.33 0.36 0.43 14666 1
## nu 18.38 0.10 13.06 3.59 8.85 14.93 24.28 52.13 17942 1
## rho -0.35 0.00 0.15 -0.62 -0.45 -0.36 -0.25 -0.02 17552 1
## cov[1,1] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 14537 1
## cov[1,2] -0.01 0.00 0.00 -0.01 -0.01 -0.01 0.00 0.00 13794 1
## cov[2,1] -0.01 0.00 0.00 -0.01 -0.01 -0.01 0.00 0.00 13794 1
## cov[2,2] 0.11 0.00 0.03 0.06 0.09 0.11 0.13 0.19 14249 1
## x_rand[1] -0.38 0.00 0.05 -0.49 -0.41 -0.38 -0.35 -0.27 15689 1
## x_rand[2] 1.82 0.00 0.38 1.08 1.59 1.82 2.05 2.57 16069 1
## lp__ 95.22 0.02 1.80 90.80 94.29 95.58 96.54 97.66 7114 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:51:37 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(COCA_spoken_Range_Log_AW_MI, MI, COCA_spoken_Range_Log_AW)
Correlational analysis on first response measures
Fluency rating (speech rate)
Fluency_Raw_first = rob.cor.mcmc(cbind(Fluency, Raw_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.3714333, SD = 0.1429251
## Posterior median and MAD: Median = -0.3805206, MAD = 0.1432005
## Rho values with 99% posterior probability: 99% HPDI = [-0.6897861, 0.02723236]
## Rho values with 95% posterior probability: 95% HPDI = [-0.6421761, -0.09231737]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.990375
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.009625
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.0364375
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.0144375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.806375
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.4456875
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0390625print(Fluency_Raw_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.52 0.00 0.03 0.47 0.50 0.52 0.54 0.58 17468 1
## mu[2] 5.97 0.00 0.10 5.79 5.91 5.97 6.04 6.16 17943 1
## sigma[1] 0.17 0.00 0.02 0.14 0.16 0.17 0.18 0.22 17238 1
## sigma[2] 0.58 0.00 0.07 0.46 0.53 0.57 0.63 0.74 16708 1
## nu 28.18 0.10 14.96 8.19 17.26 25.16 35.89 64.41 22011 1
## rho -0.37 0.00 0.14 -0.62 -0.47 -0.38 -0.28 -0.07 15548 1
## cov[1,1] 0.03 0.00 0.01 0.02 0.02 0.03 0.03 0.05 16404 1
## cov[1,2] -0.04 0.00 0.02 -0.08 -0.05 -0.04 -0.03 -0.01 12747 1
## cov[2,1] -0.04 0.00 0.02 -0.08 -0.05 -0.04 -0.03 -0.01 12747 1
## cov[2,2] 0.34 0.00 0.09 0.21 0.28 0.33 0.39 0.55 15886 1
## x_rand[1] 0.52 0.00 0.18 0.15 0.41 0.52 0.64 0.89 15769 1
## x_rand[2] 5.97 0.00 0.62 4.73 5.58 5.98 6.38 7.18 15757 1
## lp__ 27.36 0.02 1.78 23.08 26.41 27.69 28.65 29.82 7173 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:51:49 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(Fluency_Raw_first, Raw_first, Fluency)
Fluency_tscore_first = rob.cor.mcmc(cbind(Fluency, tscore_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.2568913, SD = 0.153614
## Posterior median and MAD: Median = -0.2635442, MAD = 0.1554936
## Rho values with 99% posterior probability: 99% HPDI = [-0.6131416, 0.1669564]
## Rho values with 95% posterior probability: 95% HPDI = [-0.5494539, 0.04586674]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.947375
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.052625
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.140125
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.0658125
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.537
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.1784375
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.007125print(Fluency_tscore_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.52 0.00 0.03 0.46 0.50 0.52 0.54 0.58 19678 1
## mu[2] 8.59 0.00 0.56 7.47 8.21 8.58 8.96 9.69 19965 1
## sigma[1] 0.17 0.00 0.02 0.14 0.16 0.17 0.18 0.22 17729 1
## sigma[2] 3.40 0.00 0.43 2.67 3.10 3.36 3.65 4.35 17614 1
## nu 26.90 0.10 14.92 7.43 16.07 23.71 34.34 64.35 21001 1
## rho -0.26 0.00 0.15 -0.54 -0.37 -0.26 -0.15 0.06 19883 1
## cov[1,1] 0.03 0.00 0.01 0.02 0.02 0.03 0.03 0.05 16421 1
## cov[1,2] -0.15 0.00 0.11 -0.38 -0.22 -0.15 -0.08 0.03 15795 1
## cov[2,1] -0.15 0.00 0.11 -0.38 -0.22 -0.15 -0.08 0.03 15795 1
## cov[2,2] 11.72 0.02 3.04 7.11 9.59 11.28 13.33 18.93 16422 1
## x_rand[1] 0.52 0.00 0.18 0.15 0.40 0.52 0.64 0.88 16241 1
## x_rand[2] 8.64 0.03 3.66 1.45 6.28 8.65 10.98 15.83 16689 1
## lp__ -43.44 0.02 1.79 -47.81 -44.41 -43.10 -42.14 -40.97 6747 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:52:00 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(Fluency_tscore_first, tscore_first, Fluency)
Fluency_MI_first = rob.cor.mcmc(cbind(Fluency, MI_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.06085502, SD = 0.1607068
## Posterior median and MAD: Median = 0.06310896, MAD = 0.1611896
## Rho values with 99% posterior probability: 99% HPDI = [-0.3484289, 0.4729963]
## Rho values with 95% posterior probability: 95% HPDI = [-0.247167, 0.3805372]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.350875
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.649125
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.4353125
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.2251875
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.1471875
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.017625
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 6.25e-05print(Fluency_MI_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.52 0.00 0.03 0.47 0.50 0.52 0.54 0.58 19714 1
## mu[2] 2.02 0.00 0.08 1.86 1.96 2.02 2.07 2.18 21345 1
## sigma[1] 0.17 0.00 0.02 0.14 0.16 0.17 0.18 0.22 18480 1
## sigma[2] 0.48 0.00 0.06 0.38 0.44 0.48 0.52 0.61 18443 1
## nu 27.78 0.10 15.01 7.86 16.91 24.76 35.10 65.27 21112 1
## rho 0.06 0.00 0.16 -0.26 -0.05 0.06 0.17 0.37 19213 1
## cov[1,1] 0.03 0.00 0.01 0.02 0.02 0.03 0.03 0.05 17474 1
## cov[1,2] 0.01 0.00 0.01 -0.02 0.00 0.00 0.01 0.04 15476 1
## cov[2,1] 0.01 0.00 0.01 -0.02 0.00 0.00 0.01 0.04 15476 1
## cov[2,2] 0.24 0.00 0.06 0.14 0.19 0.23 0.27 0.38 17335 1
## x_rand[1] 0.52 0.00 0.18 0.16 0.41 0.52 0.64 0.89 15173 1
## x_rand[2] 2.02 0.00 0.52 1.00 1.68 2.02 2.35 3.05 15597 1
## lp__ 31.56 0.02 1.79 27.15 30.61 31.91 32.88 34.00 7501 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:52:11 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(Fluency_MI_first, MI_first, Fluency)
Articulation Rate
ArticulationRate_Raw_first = rob.cor.mcmc(cbind(ArticulationRate, Raw_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.3121715, SD = 0.1502635
## Posterior median and MAD: Median = -0.3221759, MAD = 0.152174
## Rho values with 99% posterior probability: 99% HPDI = [-0.6560713, 0.09047442]
## Rho values with 95% posterior probability: 95% HPDI = [-0.5912842, -0.01272845]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.9735625
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.0264375
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.083125
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.037375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.673625
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.2954375
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.015375print(ArticulationRate_Raw_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
## mu[1] 108.95 0.03 4.48 100.12 106.00 108.93 111.90 117.91 17263
## mu[2] 5.96 0.00 0.10 5.78 5.90 5.96 6.03 6.16 17114
## sigma[1] 26.54 0.03 3.42 20.66 24.13 26.28 28.66 34.10 17673
## sigma[2] 0.57 0.00 0.07 0.45 0.52 0.56 0.61 0.73 17596
## nu 24.29 0.10 14.02 6.32 13.97 21.21 31.29 60.01 18923
## rho -0.31 0.00 0.15 -0.58 -0.42 -0.32 -0.21 0.01 18423
## cov[1,1] 716.17 1.45 188.22 426.67 582.33 690.39 821.15 1163.00 16838
## cov[1,2] -4.85 0.02 2.81 -11.05 -6.48 -4.62 -2.95 0.08 15235
## cov[2,1] -4.85 0.02 2.81 -11.05 -6.48 -4.62 -2.95 0.08 15235
## cov[2,2] 0.33 0.00 0.09 0.20 0.27 0.32 0.38 0.54 16969
## x_rand[1] 108.79 0.23 28.82 52.65 90.37 108.85 127.31 165.73 16041
## x_rand[2] 5.96 0.00 0.62 4.74 5.56 5.97 6.36 7.20 15825
## lp__ -170.75 0.02 1.80 -175.14 -171.68 -170.41 -169.44 -168.29 7587
## Rhat
## mu[1] 1
## mu[2] 1
## sigma[1] 1
## sigma[2] 1
## nu 1
## rho 1
## cov[1,1] 1
## cov[1,2] 1
## cov[2,1] 1
## cov[2,2] 1
## x_rand[1] 1
## x_rand[2] 1
## lp__ 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:52:22 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(ArticulationRate_Raw_first, Raw_first, ArticulationRate)
ArticulationRate_tscore_first = rob.cor.mcmc(cbind(ArticulationRate, tscore_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.1940523, SD = 0.1578336
## Posterior median and MAD: Median = -0.1998097, MAD = 0.157627
## Rho values with 99% posterior probability: 99% HPDI = [-0.5520304, 0.2315173]
## Rho values with 95% posterior probability: 95% HPDI = [-0.4897879, 0.1220478]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.88375
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.11625
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.229875
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.1131875
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.3765625
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.0924375
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.001125print(ArticulationRate_tscore_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
## mu[1] 109.01 0.03 4.40 100.30 106.04 109.00 111.96 117.71 20299
## mu[2] 8.58 0.00 0.57 7.46 8.20 8.58 8.96 9.70 19676
## sigma[1] 26.74 0.02 3.44 20.77 24.32 26.44 28.83 34.24 19180
## sigma[2] 3.39 0.00 0.43 2.66 3.09 3.35 3.65 4.34 17477
## nu 25.32 0.10 14.20 6.86 14.92 22.30 32.32 60.92 20522
## rho -0.19 0.00 0.16 -0.48 -0.30 -0.20 -0.09 0.13 18409
## cov[1,1] 726.72 1.42 191.75 431.40 591.45 699.06 831.24 1172.58 18181
## cov[1,2] -18.10 0.14 16.28 -52.68 -27.67 -17.20 -7.60 11.84 14373
## cov[2,1] -18.10 0.14 16.28 -52.68 -27.67 -17.20 -7.60 11.84 14373
## cov[2,2] 11.70 0.02 3.04 7.08 9.56 11.25 13.35 18.87 16437
## x_rand[1] 108.91 0.23 29.01 51.21 90.70 109.02 127.23 166.46 15830
## x_rand[2] 8.63 0.03 3.61 1.52 6.27 8.65 10.99 15.82 15910
## lp__ -241.33 0.02 1.78 -245.72 -242.27 -240.99 -240.02 -238.89 6875
## Rhat
## mu[1] 1
## mu[2] 1
## sigma[1] 1
## sigma[2] 1
## nu 1
## rho 1
## cov[1,1] 1
## cov[1,2] 1
## cov[2,1] 1
## cov[2,2] 1
## x_rand[1] 1
## x_rand[2] 1
## lp__ 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:52:33 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(ArticulationRate_tscore_first, tscore_first, ArticulationRate)
ArticulationRate_MI_first = rob.cor.mcmc(cbind(ArticulationRate, MI_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.01924975, SD = 0.1650138
## Posterior median and MAD: Median = 0.02122846, MAD = 0.1698644
## Rho values with 99% posterior probability: 99% HPDI = [-0.387771, 0.431698]
## Rho values with 95% posterior probability: 95% HPDI = [-0.3103074, 0.3279178]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.4499375
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.5500625
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.4401875
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.228125
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.134125
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.0134375
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 6.25e-05print(ArticulationRate_MI_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
## mu[1] 109.24 0.03 4.42 100.54 106.31 109.24 112.17 117.93 19918
## mu[2] 2.02 0.00 0.08 1.86 1.96 2.02 2.07 2.18 17830
## sigma[1] 26.70 0.03 3.47 20.72 24.27 26.39 28.80 34.36 18370
## sigma[2] 0.48 0.00 0.06 0.37 0.44 0.47 0.52 0.62 18332
## nu 24.90 0.10 14.27 6.64 14.66 21.75 31.90 60.26 19230
## rho 0.02 0.00 0.17 -0.31 -0.09 0.02 0.14 0.33 19028
## cov[1,1] 724.82 1.46 192.71 429.47 588.88 696.42 829.43 1180.90 17357
## cov[1,2] 0.26 0.02 2.27 -4.30 -1.16 0.25 1.67 4.78 15689
## cov[2,1] 0.26 0.02 2.27 -4.30 -1.16 0.25 1.67 4.78 15689
## cov[2,2] 0.23 0.00 0.06 0.14 0.19 0.23 0.27 0.38 17409
## x_rand[1] 109.41 0.23 28.71 52.35 91.05 109.68 127.77 165.75 15400
## x_rand[2] 2.01 0.00 0.53 0.96 1.68 2.01 2.35 3.07 14709
## lp__ -165.95 0.02 1.77 -170.23 -166.94 -165.63 -164.63 -163.49 7236
## Rhat
## mu[1] 1
## mu[2] 1
## sigma[1] 1
## sigma[2] 1
## nu 1
## rho 1
## cov[1,1] 1
## cov[1,2] 1
## cov[2,1] 1
## cov[2,2] 1
## x_rand[1] 1
## x_rand[2] 1
## lp__ 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:52:45 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(ArticulationRate_MI_first, MI_first, ArticulationRate)
Silent Pause ratio
SilentPause_Raw_first = rob.cor.mcmc(cbind(SilentPause, Raw_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.3293046, SD = 0.1479797
## Posterior median and MAD: Median = 0.336956, MAD = 0.1464312
## Rho values with 99% posterior probability: 99% HPDI = [-0.07243442, 0.666712]
## Rho values with 95% posterior probability: 95% HPDI = [0.04178649, 0.6124378]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.019625
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.980375
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.0685
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.0285
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.721125
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.3321875
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.02225print(SilentPause_Raw_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.59 0.00 0.04 0.52 0.57 0.59 0.62 0.66 18724 1
## mu[2] 5.96 0.00 0.10 5.78 5.90 5.96 6.03 6.16 17321 1
## sigma[1] 0.21 0.00 0.03 0.17 0.19 0.21 0.23 0.27 16383 1
## sigma[2] 0.58 0.00 0.07 0.45 0.53 0.57 0.62 0.74 17921 1
## nu 26.60 0.10 14.79 7.54 15.92 23.41 33.92 62.99 21473 1
## rho 0.33 0.00 0.15 0.02 0.23 0.34 0.43 0.59 18333 1
## cov[1,1] 0.05 0.00 0.01 0.03 0.04 0.04 0.05 0.07 15434 1
## cov[1,2] 0.04 0.00 0.02 0.00 0.03 0.04 0.06 0.09 14318 1
## cov[2,1] 0.04 0.00 0.02 0.00 0.03 0.04 0.06 0.09 14318 1
## cov[2,2] 0.34 0.00 0.09 0.21 0.28 0.33 0.39 0.55 16898 1
## x_rand[1] 0.59 0.00 0.23 0.13 0.44 0.59 0.74 1.05 15813 1
## x_rand[2] 5.97 0.01 0.63 4.73 5.57 5.97 6.37 7.22 15025 1
## lp__ 17.93 0.02 1.79 13.55 16.98 18.26 19.24 20.39 7311 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:52:58 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(SilentPause_Raw_first, Raw_first, SilentPause)
SilentPause_tscore_first = rob.cor.mcmc(cbind(SilentPause, tscore_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.2025263, SD = 0.1573282
## Posterior median and MAD: Median = 0.2071733, MAD = 0.1586361
## Rho values with 99% posterior probability: 99% HPDI = [-0.219817, 0.5629524]
## Rho values with 95% posterior probability: 95% HPDI = [-0.1078573, 0.5019379]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.101375
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.898625
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.222
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.1126875
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.398875
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.104375
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0021875print(SilentPause_tscore_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.59 0.00 0.04 0.52 0.57 0.59 0.62 0.66 18275 1
## mu[2] 8.58 0.00 0.57 7.46 8.20 8.58 8.95 9.70 20160 1
## sigma[1] 0.21 0.00 0.03 0.17 0.19 0.21 0.23 0.27 16621 1
## sigma[2] 3.40 0.00 0.43 2.65 3.10 3.36 3.66 4.35 20223 1
## nu 26.33 0.10 14.57 7.42 15.70 23.19 33.49 63.20 22077 1
## rho 0.20 0.00 0.16 -0.12 0.10 0.21 0.31 0.49 17903 1
## cov[1,1] 0.05 0.00 0.01 0.03 0.04 0.04 0.05 0.08 15668 1
## cov[1,2] 0.15 0.00 0.13 -0.08 0.06 0.14 0.23 0.44 14465 1
## cov[2,1] 0.15 0.00 0.13 -0.08 0.06 0.14 0.23 0.44 14465 1
## cov[2,2] 11.74 0.02 3.04 7.04 9.58 11.30 13.40 18.89 19291 1
## x_rand[1] 0.59 0.00 0.23 0.13 0.44 0.59 0.74 1.05 16109 1
## x_rand[2] 8.58 0.03 3.67 1.26 6.24 8.59 10.92 15.89 15578 1
## lp__ -52.80 0.02 1.77 -57.09 -53.75 -52.50 -51.49 -50.35 7361 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:53:09 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(SilentPause_tscore_first, tscore_first, SilentPause)
SilentPause_MI_first = rob.cor.mcmc(cbind(SilentPause, MI_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.04499309, SD = 0.1632741
## Posterior median and MAD: Median = -0.04562353, MAD = 0.1686032
## Rho values with 99% posterior probability: 99% HPDI = [-0.4405363, 0.3704403]
## Rho values with 95% posterior probability: 95% HPDI = [-0.3545281, 0.2754869]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.6068125
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.3931875
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.433
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.226125
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.14075
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.014875
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0print(SilentPause_MI_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.59 0.00 0.04 0.52 0.57 0.59 0.62 0.66 21554 1
## mu[2] 2.02 0.00 0.08 1.86 1.96 2.02 2.07 2.17 20777 1
## sigma[1] 0.21 0.00 0.03 0.17 0.19 0.21 0.23 0.27 18215 1
## sigma[2] 0.48 0.00 0.06 0.38 0.44 0.48 0.52 0.61 19877 1
## nu 25.51 0.10 14.09 6.90 15.25 22.63 32.60 61.19 21428 1
## rho -0.04 0.00 0.16 -0.36 -0.16 -0.05 0.07 0.27 19376 1
## cov[1,1] 0.05 0.00 0.01 0.03 0.04 0.04 0.05 0.07 17155 1
## cov[1,2] 0.00 0.00 0.02 -0.04 -0.02 0.00 0.01 0.03 15920 1
## cov[2,1] 0.00 0.00 0.02 -0.04 -0.02 0.00 0.01 0.03 15920 1
## cov[2,2] 0.24 0.00 0.06 0.14 0.19 0.23 0.27 0.38 18796 1
## x_rand[1] 0.59 0.00 0.23 0.14 0.45 0.59 0.74 1.04 16174 1
## x_rand[2] 2.02 0.00 0.52 0.96 1.69 2.03 2.36 3.04 16186 1
## lp__ 22.64 0.02 1.75 18.40 21.70 22.98 23.93 25.04 7367 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:53:20 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(SilentPause_MI_first, MI_first, SilentPause)
Filled pause ratio
FilledPause_Raw_first = rob.cor.mcmc(cbind(FilledPause, Raw_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.1729608, SD = 0.1603981
## Posterior median and MAD: Median = -0.1778422, MAD = 0.161257
## Rho values with 99% posterior probability: 99% HPDI = [-0.559818, 0.2466906]
## Rho values with 95% posterior probability: 95% HPDI = [-0.4772728, 0.1437702]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.8565625
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.1434375
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.2669375
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.132
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.333125
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.076125
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.001375print(FilledPause_Raw_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.07 0.00 0.01 0.05 0.06 0.07 0.08 0.09 21876 1
## mu[2] 5.97 0.00 0.10 5.78 5.90 5.97 6.04 6.16 21540 1
## sigma[1] 0.06 0.00 0.01 0.05 0.06 0.06 0.07 0.08 19741 1
## sigma[2] 0.58 0.00 0.07 0.45 0.53 0.57 0.62 0.74 18581 1
## nu 24.85 0.10 14.28 6.71 14.33 21.77 31.85 61.20 20811 1
## rho -0.17 0.00 0.16 -0.47 -0.28 -0.18 -0.07 0.15 19407 1
## cov[1,1] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 18801 1
## cov[1,2] -0.01 0.00 0.01 -0.02 -0.01 -0.01 0.00 0.01 16225 1
## cov[2,1] -0.01 0.00 0.01 -0.02 -0.01 -0.01 0.00 0.01 16225 1
## cov[2,2] 0.34 0.00 0.09 0.20 0.28 0.33 0.39 0.55 17542 1
## x_rand[1] 0.07 0.00 0.07 -0.06 0.03 0.07 0.11 0.20 15372 1
## x_rand[2] 5.98 0.00 0.62 4.73 5.59 5.98 6.37 7.20 15627 1
## lp__ 64.67 0.02 1.79 60.32 63.72 65.00 66.00 67.14 6573 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:53:32 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(FilledPause_Raw_first, Raw_first, FilledPause)
FilledPause_tscore_first = rob.cor.mcmc(cbind(FilledPause, tscore_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.2925439, SD = 0.1512972
## Posterior median and MAD: Median = -0.2999707, MAD = 0.1499616
## Rho values with 99% posterior probability: 99% HPDI = [-0.6508023, 0.1171802]
## Rho values with 95% posterior probability: 95% HPDI = [-0.5703691, 0.01939991]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.9641875
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.0358125
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.0975
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.0456875
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.6310625
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.24525
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0125print(FilledPause_Raw_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.07 0.00 0.01 0.05 0.06 0.07 0.08 0.09 21876 1
## mu[2] 5.97 0.00 0.10 5.78 5.90 5.97 6.04 6.16 21540 1
## sigma[1] 0.06 0.00 0.01 0.05 0.06 0.06 0.07 0.08 19741 1
## sigma[2] 0.58 0.00 0.07 0.45 0.53 0.57 0.62 0.74 18581 1
## nu 24.85 0.10 14.28 6.71 14.33 21.77 31.85 61.20 20811 1
## rho -0.17 0.00 0.16 -0.47 -0.28 -0.18 -0.07 0.15 19407 1
## cov[1,1] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 18801 1
## cov[1,2] -0.01 0.00 0.01 -0.02 -0.01 -0.01 0.00 0.01 16225 1
## cov[2,1] -0.01 0.00 0.01 -0.02 -0.01 -0.01 0.00 0.01 16225 1
## cov[2,2] 0.34 0.00 0.09 0.20 0.28 0.33 0.39 0.55 17542 1
## x_rand[1] 0.07 0.00 0.07 -0.06 0.03 0.07 0.11 0.20 15372 1
## x_rand[2] 5.98 0.00 0.62 4.73 5.59 5.98 6.37 7.20 15627 1
## lp__ 64.67 0.02 1.79 60.32 63.72 65.00 66.00 67.14 6573 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:53:32 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(FilledPause_tscore_first, tscore_first, FilledPause)
FilledPause_MI_first = rob.cor.mcmc(cbind(FilledPause, MI_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.2554604, SD = 0.158861
## Posterior median and MAD: Median = -0.2627012, MAD = 0.1608616
## Rho values with 99% posterior probability: 99% HPDI = [-0.6221882, 0.1723432]
## Rho values with 95% posterior probability: 95% HPDI = [-0.5669873, 0.0478328]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.94025
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.05975
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.147375
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.0689375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.530875
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.18525
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0070625print(FilledPause_MI_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.07 0.00 0.01 0.05 0.06 0.07 0.07 0.09 17430 1
## mu[2] 2.02 0.00 0.08 1.87 1.97 2.02 2.08 2.18 18514 1
## sigma[1] 0.06 0.00 0.01 0.05 0.05 0.06 0.07 0.08 15993 1
## sigma[2] 0.47 0.00 0.06 0.36 0.43 0.47 0.51 0.61 15824 1
## nu 22.41 0.10 13.82 5.19 12.40 19.29 29.03 57.52 18089 1
## rho -0.26 0.00 0.16 -0.54 -0.37 -0.26 -0.15 0.07 17414 1
## cov[1,1] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 15823 1
## cov[1,2] -0.01 0.00 0.01 -0.02 -0.01 -0.01 0.00 0.00 14120 1
## cov[2,1] -0.01 0.00 0.01 -0.02 -0.01 -0.01 0.00 0.00 14120 1
## cov[2,2] 0.23 0.00 0.06 0.13 0.18 0.22 0.26 0.37 15270 1
## x_rand[1] 0.07 0.00 0.07 -0.06 0.03 0.07 0.11 0.20 15733 1
## x_rand[2] 2.02 0.00 0.52 0.98 1.70 2.02 2.35 3.05 15743 1
## lp__ 72.82 0.02 1.80 68.44 71.86 73.16 74.12 75.31 7232 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:53:58 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(FilledPause_MI_first, MI_first, FilledPause)
Richness rating
Richness_Raw_first = rob.cor.mcmc(cbind(Richness, Raw_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.2615031, SD = 0.1532825
## Posterior median and MAD: Median = -0.2680534, MAD = 0.1543734
## Rho values with 99% posterior probability: 99% HPDI = [-0.6390891, 0.1408571]
## Rho values with 95% posterior probability: 95% HPDI = [-0.5515097, 0.04168982]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.9489375
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.0510625
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.1360625
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.0626875
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.5460625
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.1865
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0070625print(Richness_Raw_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.42 0.00 0.02 0.38 0.41 0.42 0.43 0.46 16493 1
## mu[2] 5.97 0.00 0.10 5.79 5.91 5.97 6.04 6.16 17806 1
## sigma[1] 0.13 0.00 0.02 0.10 0.11 0.12 0.14 0.16 16472 1
## sigma[2] 0.58 0.00 0.07 0.46 0.53 0.57 0.63 0.75 17729 1
## nu 28.35 0.11 15.14 8.20 17.30 25.25 36.13 65.40 19616 1
## rho -0.26 0.00 0.15 -0.54 -0.37 -0.27 -0.16 0.05 18285 1
## cov[1,1] 0.02 0.00 0.00 0.01 0.01 0.02 0.02 0.03 15735 1
## cov[1,2] -0.02 0.00 0.01 -0.05 -0.03 -0.02 -0.01 0.00 14582 1
## cov[2,1] -0.02 0.00 0.01 -0.05 -0.03 -0.02 -0.01 0.00 14582 1
## cov[2,2] 0.34 0.00 0.09 0.21 0.28 0.33 0.39 0.56 16593 1
## x_rand[1] 0.42 0.00 0.14 0.15 0.33 0.42 0.51 0.69 15748 1
## x_rand[2] 5.98 0.00 0.62 4.74 5.59 5.97 6.38 7.21 16235 1
## lp__ 37.84 0.02 1.81 33.35 36.90 38.20 39.16 40.29 6943 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:54:09 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(Richness_Raw_first, Raw_first, Richness)
Richness_tscore_first = rob.cor.mcmc(cbind(Richness, tscore_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.09007894, SD = 0.1626942
## Posterior median and MAD: Median = 0.09240826, MAD = 0.1668717
## Rho values with 99% posterior probability: 99% HPDI = [-0.3180514, 0.4987509]
## Rho values with 95% posterior probability: 95% HPDI = [-0.2254739, 0.4031996]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.291
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.709
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.39075
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.199375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.1874375
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.026375
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0003125print(Richness_tscore_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.42 0.00 0.02 0.38 0.41 0.42 0.43 0.46 18224 1
## mu[2] 8.62 0.00 0.57 7.50 8.24 8.62 8.99 9.76 20104 1
## sigma[1] 0.13 0.00 0.02 0.10 0.11 0.12 0.14 0.16 18479 1
## sigma[2] 3.42 0.00 0.44 2.68 3.11 3.37 3.68 4.36 19793 1
## nu 27.20 0.10 14.72 7.69 16.54 24.20 34.72 64.15 20400 1
## rho 0.09 0.00 0.16 -0.23 -0.02 0.09 0.20 0.40 19161 1
## cov[1,1] 0.02 0.00 0.00 0.01 0.01 0.02 0.02 0.03 17740 1
## cov[1,2] 0.04 0.00 0.08 -0.11 -0.01 0.04 0.09 0.19 15954 1
## cov[2,1] 0.04 0.00 0.08 -0.11 -0.01 0.04 0.09 0.19 15954 1
## cov[2,2] 11.86 0.02 3.12 7.16 9.65 11.38 13.54 19.05 18516 1
## x_rand[1] 0.42 0.00 0.14 0.15 0.33 0.42 0.51 0.69 15943 1
## x_rand[2] 8.60 0.03 3.67 1.39 6.25 8.55 10.95 15.84 15939 1
## lp__ -32.69 0.02 1.78 -36.96 -33.66 -32.36 -31.38 -30.23 7608 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:54:20 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(Richness_tscore_first, tscore_first, Richness)
Richness_MI_first = rob.cor.mcmc(cbind(Richness, MI_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.3442574, SD = 0.1452182
## Posterior median and MAD: Median = 0.3516802, MAD = 0.1434889
## Rho values with 99% posterior probability: 99% HPDI = [-0.0528074, 0.6800495]
## Rho values with 95% posterior probability: 95% HPDI = [0.05962729, 0.6212149]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.0149375
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.9850625
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.0525
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.0230625
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.7533125
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.3684375
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.026625print(Richness_MI_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.42 0.00 0.02 0.38 0.40 0.42 0.43 0.46 17183 1
## mu[2] 2.02 0.00 0.08 1.87 1.97 2.02 2.08 2.18 16208 1
## sigma[1] 0.13 0.00 0.02 0.10 0.11 0.12 0.13 0.16 16605 1
## sigma[2] 0.48 0.00 0.06 0.38 0.44 0.48 0.52 0.62 17237 1
## nu 26.98 0.11 14.57 7.63 16.26 24.03 34.49 62.90 19067 1
## rho 0.34 0.00 0.15 0.04 0.25 0.35 0.45 0.60 17965 1
## cov[1,1] 0.02 0.00 0.00 0.01 0.01 0.02 0.02 0.03 15899 1
## cov[1,2] 0.02 0.00 0.01 0.00 0.01 0.02 0.03 0.05 14008 1
## cov[2,1] 0.02 0.00 0.01 0.00 0.01 0.02 0.03 0.05 14008 1
## cov[2,2] 0.24 0.00 0.06 0.14 0.19 0.23 0.27 0.38 16734 1
## x_rand[1] 0.42 0.00 0.13 0.15 0.33 0.42 0.50 0.68 15343 1
## x_rand[2] 2.02 0.00 0.51 1.00 1.69 2.02 2.35 3.05 16368 1
## lp__ 46.22 0.02 1.77 41.92 45.28 46.55 47.53 48.66 7784 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:54:31 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(Richness_MI_first, MI_first, Richness)
Diversity
MTLD_Raw_first = rob.cor.mcmc(cbind(MTLD, Raw_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.2074678, SD = 0.1576626
## Posterior median and MAD: Median = -0.2132759, MAD = 0.1590066
## Rho values with 99% posterior probability: 99% HPDI = [-0.5768855, 0.2157282]
## Rho values with 95% posterior probability: 95% HPDI = [-0.5074492, 0.09887879]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.9011875
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.0988125
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.215625
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.106375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.4120625
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.1105625
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0025print(MTLD_Raw_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
## mu[1] 37.07 0.01 1.72 33.69 35.94 37.07 38.21 40.51 20230
## mu[2] 5.98 0.00 0.10 5.79 5.91 5.98 6.04 6.16 18987
## sigma[1] 10.36 0.01 1.31 8.15 9.44 10.24 11.15 13.26 18505
## sigma[2] 0.58 0.00 0.07 0.46 0.53 0.57 0.62 0.74 18734
## nu 27.22 0.10 14.72 7.52 16.42 24.26 34.85 64.00 21474
## rho -0.21 0.00 0.16 -0.50 -0.32 -0.21 -0.10 0.11 20159
## cov[1,1] 109.02 0.21 28.30 66.35 89.08 104.83 124.36 175.85 17345
## cov[1,2] -1.28 0.01 1.09 -3.67 -1.91 -1.21 -0.57 0.67 16335
## cov[2,1] -1.28 0.01 1.09 -3.67 -1.91 -1.21 -0.57 0.67 16335
## cov[2,2] 0.34 0.00 0.09 0.21 0.28 0.33 0.39 0.55 17642
## x_rand[1] 37.02 0.09 11.17 14.79 29.89 37.02 44.18 58.79 16270
## x_rand[2] 5.98 0.00 0.63 4.75 5.58 5.98 6.38 7.23 16096
## lp__ -134.99 0.02 1.79 -139.30 -135.93 -134.66 -133.68 -132.54 7365
## Rhat
## mu[1] 1
## mu[2] 1
## sigma[1] 1
## sigma[2] 1
## nu 1
## rho 1
## cov[1,1] 1
## cov[1,2] 1
## cov[2,1] 1
## cov[2,2] 1
## x_rand[1] 1
## x_rand[2] 1
## lp__ 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:54:42 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(MTLD_Raw_first, Raw_first, MTLD)
MTLD_tscore_first = rob.cor.mcmc(cbind(MTLD, tscore_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.03919154, SD = 0.1616442
## Posterior median and MAD: Median = -0.03731191, MAD = 0.1649856
## Rho values with 99% posterior probability: 99% HPDI = [-0.4383311, 0.371957]
## Rho values with 95% posterior probability: 95% HPDI = [-0.3586273, 0.2680975]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.592625
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.407375
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.4440625
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.2366875
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.1360625
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.0138125
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0001875print(MTLD_tscore_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
## mu[1] 36.88 0.01 1.71 33.49 35.74 36.88 38.01 40.25 20185
## mu[2] 8.60 0.00 0.57 7.49 8.24 8.60 8.97 9.72 21365
## sigma[1] 10.40 0.01 1.31 8.18 9.46 10.27 11.21 13.26 20597
## sigma[2] 3.41 0.00 0.44 2.67 3.10 3.37 3.67 4.37 20334
## nu 26.46 0.09 14.48 7.62 15.89 23.36 33.65 62.61 23538
## rho -0.04 0.00 0.16 -0.35 -0.15 -0.04 0.07 0.28 20618
## cov[1,1] 109.78 0.20 28.29 66.89 89.48 105.41 125.65 175.75 19290
## cov[1,2] -1.42 0.05 6.16 -13.92 -5.16 -1.25 2.35 10.65 15753
## cov[2,1] -1.42 0.05 6.16 -13.92 -5.16 -1.25 2.35 10.65 15753
## cov[2,2] 11.80 0.02 3.11 7.15 9.59 11.36 13.47 19.09 18865
## x_rand[1] 36.97 0.09 11.22 14.34 29.97 37.11 44.16 59.13 15769
## x_rand[2] 8.60 0.03 3.69 1.33 6.26 8.59 10.93 15.87 16046
## lp__ -205.06 0.02 1.77 -209.40 -206.01 -204.72 -203.76 -202.60 6946
## Rhat
## mu[1] 1
## mu[2] 1
## sigma[1] 1
## sigma[2] 1
## nu 1
## rho 1
## cov[1,1] 1
## cov[1,2] 1
## cov[2,1] 1
## cov[2,2] 1
## x_rand[1] 1
## x_rand[2] 1
## lp__ 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:54:53 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(MTLD_tscore_first, tscore_first, MTLD)
MTLD_MI_first = rob.cor.mcmc(cbind(MTLD, MI_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.1532119, SD = 0.1582243
## Posterior median and MAD: Median = 0.1576082, MAD = 0.1609928
## Rho values with 99% posterior probability: 99% HPDI = [-0.2620053, 0.5301753]
## Rho values with 95% posterior probability: 95% HPDI = [-0.1605513, 0.4554807]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.1685625
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.8314375
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.3030625
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.1524375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.28225
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.0565
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0008125print(MTLD_MI_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
## mu[1] 36.96 0.01 1.72 33.58 35.84 36.95 38.10 40.34 20277
## mu[2] 2.02 0.00 0.08 1.87 1.97 2.02 2.08 2.18 20461
## sigma[1] 10.39 0.01 1.32 8.17 9.47 10.27 11.20 13.29 19575
## sigma[2] 0.49 0.00 0.06 0.38 0.44 0.48 0.52 0.62 19994
## nu 27.55 0.10 14.54 8.15 16.83 24.65 35.16 62.81 21333
## rho 0.15 0.00 0.16 -0.16 0.05 0.16 0.26 0.45 19988
## cov[1,1] 109.77 0.21 28.50 66.71 89.76 105.46 125.48 176.75 18247
## cov[1,2] 0.80 0.01 0.89 -0.85 0.22 0.76 1.31 2.70 16701
## cov[2,1] 0.80 0.01 0.89 -0.85 0.22 0.76 1.31 2.70 16701
## cov[2,2] 0.24 0.00 0.06 0.15 0.20 0.23 0.27 0.39 18733
## x_rand[1] 37.01 0.09 11.18 14.86 29.93 37.04 44.02 59.21 15940
## x_rand[2] 2.03 0.00 0.52 0.99 1.69 2.03 2.36 3.05 16245
## lp__ -128.36 0.02 1.76 -132.60 -129.30 -128.06 -127.06 -125.93 7412
## Rhat
## mu[1] 1
## mu[2] 1
## sigma[1] 1
## sigma[2] 1
## nu 1
## rho 1
## cov[1,1] 1
## cov[1,2] 1
## cov[2,1] 1
## cov[2,2] 1
## x_rand[1] 1
## x_rand[2] 1
## lp__ 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:55:04 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(MTLD_MI_first, MI_first, MTLD)
Frequency
COCA_spoken_Frequency_Log_AW_Raw_first = rob.cor.mcmc(cbind(COCA_spoken_Frequency_Log_AW, Raw_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.08567511, SD = 0.1637677
## Posterior median and MAD: Median = 0.0893334, MAD = 0.1668686
## Rho values with 99% posterior probability: 99% HPDI = [-0.3269144, 0.4899783]
## Rho values with 95% posterior probability: 95% HPDI = [-0.2313197, 0.4036786]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.3020625
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.6979375
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.3953125
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.2044375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.1790625
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.02525
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.000375print(COCA_spoken_Frequency_Log_AW_Raw_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 3.16 0.00 0.01 3.14 3.16 3.16 3.17 3.19 18325 1
## mu[2] 5.97 0.00 0.10 5.78 5.90 5.96 6.03 6.16 18253 1
## sigma[1] 0.08 0.00 0.01 0.06 0.08 0.08 0.09 0.11 16479 1
## sigma[2] 0.58 0.00 0.07 0.45 0.52 0.57 0.62 0.74 18095 1
## nu 22.93 0.10 14.17 5.19 12.53 19.60 29.89 58.50 19347 1
## rho 0.09 0.00 0.16 -0.24 -0.03 0.09 0.20 0.40 18205 1
## cov[1,1] 0.01 0.00 0.00 0.00 0.01 0.01 0.01 0.01 15984 1
## cov[1,2] 0.00 0.00 0.01 -0.01 0.00 0.00 0.01 0.02 14780 1
## cov[2,1] 0.00 0.00 0.01 -0.01 0.00 0.00 0.01 0.02 14780 1
## cov[2,2] 0.34 0.00 0.09 0.20 0.27 0.33 0.39 0.55 17216 1
## x_rand[1] 3.16 0.00 0.09 2.98 3.11 3.16 3.22 3.35 15840 1
## x_rand[2] 5.96 0.01 0.64 4.69 5.57 5.97 6.36 7.22 15338 1
## lp__ 50.83 0.02 1.78 46.46 49.87 51.15 52.15 53.28 7669 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:55:16 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(COCA_spoken_Frequency_Log_AW_Raw_first, Raw_first, COCA_spoken_Frequency_Log_AW)
COCA_spoken_Frequency_Log_AW_tscore_first = rob.cor.mcmc(cbind(COCA_spoken_Frequency_Log_AW, tscore_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.03696373, SD = 0.169242
## Posterior median and MAD: Median = 0.04004806, MAD = 0.1738711
## Rho values with 99% posterior probability: 99% HPDI = [-0.3965147, 0.4514541]
## Rho values with 95% posterior probability: 95% HPDI = [-0.3056386, 0.3489206]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.413875
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.586125
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.4248125
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.2146875
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.150875
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.01775
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.000125print(COCA_spoken_Frequency_Log_AW_tscore_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 3.17 0.00 0.01 3.14 3.16 3.17 3.18 3.19 19050 1
## mu[2] 8.63 0.00 0.56 7.53 8.26 8.62 9.00 9.74 20099 1
## sigma[1] 0.08 0.00 0.01 0.06 0.07 0.08 0.09 0.11 16314 1
## sigma[2] 3.32 0.00 0.44 2.56 3.02 3.29 3.59 4.31 18067 1
## nu 20.02 0.10 13.04 4.62 10.61 16.78 25.98 54.00 18416 1
## rho 0.04 0.00 0.17 -0.29 -0.08 0.04 0.16 0.36 17366 1
## cov[1,1] 0.01 0.00 0.00 0.00 0.01 0.01 0.01 0.01 15820 1
## cov[1,2] 0.01 0.00 0.05 -0.09 -0.02 0.01 0.04 0.11 13103 1
## cov[2,1] 0.01 0.00 0.05 -0.09 -0.02 0.01 0.04 0.11 13103 1
## cov[2,2] 11.25 0.02 3.06 6.54 9.12 10.79 12.90 18.55 17545 1
## x_rand[1] 3.17 0.00 0.09 2.98 3.11 3.17 3.22 3.35 16490 1
## x_rand[2] 8.64 0.03 3.67 1.31 6.32 8.63 10.97 15.91 16183 1
## lp__ -18.08 0.02 1.80 -22.40 -19.01 -17.74 -16.76 -15.62 7248 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:55:28 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(COCA_spoken_Frequency_Log_AW_tscore_first, tscore_first, COCA_spoken_Frequency_Log_AW)
COCA_spoken_Frequency_Log_AW_MI_first = rob.cor.mcmc(cbind(COCA_spoken_Frequency_Log_AW, MI_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.3604089, SD = 0.1481354
## Posterior median and MAD: Median = -0.368041, MAD = 0.1478013
## Rho values with 99% posterior probability: 99% HPDI = [-0.6982399, 0.03998982]
## Rho values with 95% posterior probability: 95% HPDI = [-0.6356368, -0.06681188]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.988
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.012
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.0458125
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.0186875
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.7799375
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.414125
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0409375print(COCA_spoken_Frequency_Log_AW_MI_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 3.17 0.00 0.01 3.14 3.16 3.17 3.18 3.19 17997 1
## mu[2] 2.03 0.00 0.08 1.87 1.97 2.03 2.08 2.18 17953 1
## sigma[1] 0.08 0.00 0.01 0.06 0.07 0.08 0.09 0.11 17004 1
## sigma[2] 0.47 0.00 0.06 0.37 0.43 0.47 0.51 0.61 16195 1
## nu 19.90 0.09 12.71 4.96 10.71 16.70 25.65 52.77 19200 1
## rho -0.36 0.00 0.15 -0.63 -0.47 -0.37 -0.27 -0.05 18851 1
## cov[1,1] 0.01 0.00 0.00 0.00 0.01 0.01 0.01 0.01 16638 1
## cov[1,2] -0.01 0.00 0.01 -0.03 -0.02 -0.01 -0.01 0.00 14613 1
## cov[2,1] -0.01 0.00 0.01 -0.03 -0.02 -0.01 -0.01 0.00 14613 1
## cov[2,2] 0.23 0.00 0.06 0.14 0.19 0.22 0.26 0.37 15555 1
## x_rand[1] 3.17 0.00 0.09 2.99 3.11 3.17 3.22 3.35 15258 1
## x_rand[2] 2.03 0.00 0.53 0.99 1.70 2.03 2.36 3.06 16317 1
## lp__ 60.75 0.02 1.76 56.41 59.83 61.07 62.03 63.17 7499 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:55:41 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(COCA_spoken_Frequency_Log_AW_MI_first, MI_first, COCA_spoken_Frequency_Log_AW)
Range
COCA_spoken_Range_Log_AW_Raw_first = rob.cor.mcmc(cbind(COCA_spoken_Range_Log_AW, Raw_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.1224214, SD = 0.1646321
## Posterior median and MAD: Median = 0.1274023, MAD = 0.1658748
## Rho values with 99% posterior probability: 99% HPDI = [-0.3086172, 0.5208941]
## Rho values with 95% posterior probability: 95% HPDI = [-0.212691, 0.4267344]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.229375
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.770625
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.340125
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.1750625
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.23625
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.040625
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.00075print(COCA_spoken_Range_Log_AW_Raw_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] -0.38 0.00 0.01 -0.40 -0.39 -0.38 -0.37 -0.36 20609 1
## mu[2] 5.96 0.00 0.10 5.77 5.90 5.96 6.03 6.16 20638 1
## sigma[1] 0.05 0.00 0.01 0.04 0.04 0.05 0.05 0.06 18612 1
## sigma[2] 0.58 0.00 0.07 0.45 0.53 0.57 0.62 0.74 18031 1
## nu 23.21 0.10 14.10 5.59 12.88 19.82 30.11 58.76 19714 1
## rho 0.12 0.00 0.16 -0.21 0.01 0.13 0.24 0.43 20027 1
## cov[1,1] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 17995 1
## cov[1,2] 0.00 0.00 0.01 -0.01 0.00 0.00 0.01 0.01 15789 1
## cov[2,1] 0.00 0.00 0.01 -0.01 0.00 0.00 0.01 0.01 15789 1
## cov[2,2] 0.34 0.00 0.09 0.20 0.28 0.33 0.39 0.55 17406 1
## x_rand[1] -0.38 0.00 0.05 -0.49 -0.41 -0.38 -0.35 -0.27 15137 1
## x_rand[2] 5.97 0.01 0.64 4.72 5.58 5.97 6.36 7.23 16080 1
## lp__ 72.19 0.02 1.82 67.69 71.24 72.54 73.51 74.64 6918 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:55:54 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(COCA_spoken_Range_Log_AW_Raw_first, Raw_first, COCA_spoken_Range_Log_AW)
COCA_spoken_Range_Log_AW_tscore_first = rob.cor.mcmc(cbind(COCA_spoken_Range_Log_AW, tscore_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = 0.08569614, SD = 0.1691503
## Posterior median and MAD: Median = 0.08676981, MAD = 0.1725701
## Rho values with 99% posterior probability: 99% HPDI = [-0.3566329, 0.4961165]
## Rho values with 95% posterior probability: 95% HPDI = [-0.2430071, 0.4128742]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.3108125
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.6891875
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.3899375
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.202375
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.193375
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.0310625
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.0005625print(COCA_spoken_Range_Log_AW_Raw_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] -0.38 0.00 0.01 -0.40 -0.39 -0.38 -0.37 -0.36 20609 1
## mu[2] 5.96 0.00 0.10 5.77 5.90 5.96 6.03 6.16 20638 1
## sigma[1] 0.05 0.00 0.01 0.04 0.04 0.05 0.05 0.06 18612 1
## sigma[2] 0.58 0.00 0.07 0.45 0.53 0.57 0.62 0.74 18031 1
## nu 23.21 0.10 14.10 5.59 12.88 19.82 30.11 58.76 19714 1
## rho 0.12 0.00 0.16 -0.21 0.01 0.13 0.24 0.43 20027 1
## cov[1,1] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 17995 1
## cov[1,2] 0.00 0.00 0.01 -0.01 0.00 0.00 0.01 0.01 15789 1
## cov[2,1] 0.00 0.00 0.01 -0.01 0.00 0.00 0.01 0.01 15789 1
## cov[2,2] 0.34 0.00 0.09 0.20 0.28 0.33 0.39 0.55 17406 1
## x_rand[1] -0.38 0.00 0.05 -0.49 -0.41 -0.38 -0.35 -0.27 15137 1
## x_rand[2] 5.97 0.01 0.64 4.72 5.58 5.97 6.36 7.23 16080 1
## lp__ 72.19 0.02 1.82 67.69 71.24 72.54 73.51 74.64 6918 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:55:54 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(COCA_spoken_Range_Log_AW_tscore_first, tscore_first, COCA_spoken_Range_Log_AW)
COCA_spoken_Range_Log_AW_MI_first = rob.cor.mcmc(cbind(COCA_spoken_Range_Log_AW, MI_first), iter=5000, warmup=1000, chains=4)
## POSTERIOR STATISTICS OF RHO
## Posterior mean and standard deviation: Mean = -0.2792651, SD = 0.157066
## Posterior median and MAD: Median = -0.2869979, MAD = 0.1582793
## Rho values with 99% posterior probability: 99% HPDI = [-0.6514037, 0.130684]
## Rho values with 95% posterior probability: 95% HPDI = [-0.5669231, 0.04044759]
## Posterior probability that rho is ≤0 (probability of positive direction): P(rho ≤ 0) = 0.9551875
## Posterior probability that rho is ≥0 (probability of negative direction): P(rho ≥ 0) = 0.0448125
## Posterior probability that rho is weak: P(-0.1 < rho < 0.1) = 0.1186875
## Posterior probability that rho is within ROPE, or % in ROPE: P(-0.05 < rho < 0.05) = 0.0545
##
## *Following Plonsky and Oswald’s (2014) benchmark:
## Posterior probability that rho is beyond small: P(abs(rho) > .25) = 0.5903125
## Posterior probability that rho is beyond medium: P(abs(rho) > .40) = 0.2291875
## Posterior probability that rho is beyond large: P(abs(rho) > .60) = 0.01225print(COCA_spoken_Range_Log_AW_MI_first)## Inference for Stan model: robust_correlation.
## 4 chains, each with iter=5000; warmup=1000; thin=1;
## post-warmup draws per chain=4000, total post-warmup draws=16000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] -0.38 0.00 0.01 -0.40 -0.39 -0.38 -0.37 -0.36 17759 1
## mu[2] 2.02 0.00 0.08 1.86 1.97 2.02 2.08 2.18 17712 1
## sigma[1] 0.05 0.00 0.01 0.04 0.04 0.05 0.05 0.06 14775 1
## sigma[2] 0.47 0.00 0.06 0.36 0.43 0.46 0.51 0.61 17192 1
## nu 18.49 0.10 12.61 4.12 9.45 14.98 24.18 50.89 16011 1
## rho -0.28 0.00 0.16 -0.56 -0.39 -0.29 -0.18 0.05 17528 1
## cov[1,1] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 14718 1
## cov[1,2] -0.01 0.00 0.00 -0.02 -0.01 -0.01 0.00 0.00 14166 1
## cov[2,1] -0.01 0.00 0.00 -0.02 -0.01 -0.01 0.00 0.00 14166 1
## cov[2,2] 0.22 0.00 0.06 0.13 0.18 0.21 0.26 0.37 16467 1
## x_rand[1] -0.38 0.00 0.05 -0.48 -0.41 -0.38 -0.35 -0.27 15929 1
## x_rand[2] 2.02 0.00 0.53 0.96 1.69 2.02 2.35 3.05 15852 1
## lp__ 80.95 0.02 1.79 76.57 80.02 81.31 82.27 83.40 6918 1
##
## Samples were drawn using NUTS(diag_e) at Sun Dec 13 18:56:20 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).posterior_scatter(COCA_spoken_Range_Log_AW_MI_first, MI_first, COCA_spoken_Range_Log_AW)
Bayesian regression with brms
get_prior(Fluency ~ Raw_first + scale(IndexCOCA_spoken_Frequency_Log_AW), data = data,
family = gaussian())## prior class coef group
## 1 b
## 2 b Raw_first
## 3 b scaleIndexCOCA_spoken_Frequency_Log_AW
## 4 student_t(3, 0.5, 2.5) Intercept
## 5 student_t(3, 0, 2.5) sigma
## resp dpar nlpar bound
## 1
## 2
## 3
## 4
## 5Oral Fluency
Flunecy rating
get_prior(scale(Fluency) ~ scale(Raw_first) + scale(IndexCOCA_spoken_Frequency_Log_AW), data = data,
family = gaussian())## prior class coef
## 1 b
## 2 b scaleIndexCOCA_spoken_Frequency_Log_AW
## 3 b scaleRaw_first
## 4 student_t(3, -0.1, 2.5) Intercept
## 5 student_t(3, 0, 2.5) sigma
## group resp dpar nlpar bound
## 1
## 2
## 3
## 4
## 5ggplot(data = data, aes(x = Raw_first, y = Fluency))+
geom_point() +
geom_smooth()
fluency0 <- brm(scale(Fluency) ~ 1 , data = data,
family = gaussian(),
save_all_pars = T,
iter = iter1, warmup = 1000, chains = 4, seed = 1234)fluency1.wp <- brm(scale(Fluency) ~ scale(Raw_first), data = data,
family = gaussian(),
prior = weak_prior,
save_all_pars = T,
iter = iter1, warmup = 1000, chains = 4, seed = 1234)
print(summary(fluency1.wp), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(Fluency) ~ scale(Raw_first)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.00133 0.15312 -0.30953 0.30229 0.99989 13926 10520
## scaleRaw_first -0.37623 0.15387 -0.67745 -0.07337 1.00012 14465 10682
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.96352 0.11623 0.76844 1.22631 1.00030 12801 10645
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(fluency1.wp)
bayes_R2(fluency1.wp)## Estimate Est.Error Q2.5 Q97.5
## R2 0.1490404 0.08776529 0.006286335 0.3294695conditional_effects(fluency1.wp)
fluency2.wp <- brm(scale(Fluency) ~ scale(Raw_first) + scale(IndexCOCA_spoken_Frequency_Log_AW), data = data,
family = gaussian(),
prior = weak_prior,
save_all_pars = T,
iter = iter1, warmup = 1000, chains = 4, seed = 1234)
print(summary(fluency2.wp), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(Fluency) ~ scale(Raw_first) + scale(IndexCOCA_spoken_Frequency_Log_AW)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept -0.00025 0.15062 -0.29991 0.29575
## scaleRaw_first -0.27151 0.18083 -0.62698 0.08694
## scaleIndexCOCA_spoken_Frequency_Log_AW -0.19981 0.18001 -0.55025 0.15885
## Rhat Bulk_ESS Tail_ESS
## Intercept 1.00030 14746 10009
## scaleRaw_first 0.99995 13902 11152
## scaleIndexCOCA_spoken_Frequency_Log_AW 1.00015 13833 11513
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.95994 0.11544 0.76648 1.21740 1.00034 13378 11252
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(fluency2.wp)
bayes_R2(fluency2.wp)## Estimate Est.Error Q2.5 Q97.5
## R2 0.1897306 0.08997675 0.02814451 0.3676389conditional_effects(fluency2.wp)
model_comp(fluency0, fluency1.wp, fluency2.wp)## [[1]]
## elpd_diff se_diff elpd_loo se_elpd_loo p_loo se_p_loo looic
## Model_1 0.000000 0.000000 -55.84954 3.348564 2.329352 0.4639848 111.6991
## Model_2 -0.527218 1.482041 -56.37676 3.290685 3.539986 0.7205831 112.7535
## Null_Model -2.182007 2.288949 -58.03154 3.081919 1.421840 0.2365736 116.0631
## se_looic
## Model_1 6.697128
## Model_2 6.581370
## Null_Model 6.163839
##
## [[2]]
## elpd_diff se_diff elpd_waic se_elpd_waic p_waic se_p_waic
## Model_1 0.0000000 0.000000 -55.83033 3.342733 2.310142 0.4565385
## Model_2 -0.4846285 1.471346 -56.31496 3.273152 3.478186 0.6959414
## Null_Model -2.1974237 2.283824 -58.02775 3.080847 1.418047 0.2353892
## waic se_waic
## Model_1 111.6607 6.685467
## Model_2 112.6299 6.546303
## Null_Model 116.0555 6.161693
##
## [[3]]
##
## [[4]]
loo_model_weights(fluency0, fluency1.wp, fluency2.wp, model_names = NULL)## Method: stacking
## ------
## weight
## fluency0 0.049
## fluency1.wp 0.748
## fluency2.wp 0.203fluency_ave <- posterior_average(fluency1.wp, fluency2.wp, weights = "stacking")
quantile(fluency_ave$b_scaleRaw_first, prob = c(.025, .975))## 2.5% 97.5%
## -0.664859216 -0.004306449mcmc_areas(fluency_ave, pars = "b_scaleRaw_first", prob = .95)+
labs(x = "Regression coefficent (std)") 
Articulation Rate
get_prior(scale(ArticulationRate) ~ scale(Raw_first) + scale(tscore_first) + scale(IndexCOCA_spoken_Frequency_Log_AW), data = data,
family = gaussian()
)## prior class coef group
## 1 b
## 2 b scaleIndexCOCA_spoken_Frequency_Log_AW
## 3 b scaleRaw_first
## 4 b scaletscore_first
## 5 student_t(3, 0, 2.5) Intercept
## 6 student_t(3, 0, 2.5) sigma
## resp dpar nlpar bound
## 1
## 2
## 3
## 4
## 5
## 6ggplot(data = data, aes(x = log(Raw_first), y = ArticulationRate))+
geom_point() +
geom_smooth()
ArtRate0 <- brm(scale(ArticulationRate) ~ 1 , data = data,
family = gaussian(),
iter = iter1, warmup = 1000, chains = 4, seed = 1234)ArtRate1 <- brm(scale(ArticulationRate) ~ scale(Raw_first) , data = data,
family = gaussian(),
prior = weak_prior,
iter = iter1, warmup = 1000, chains = 4, seed = 1234)
print(summary(ArtRate1), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(ArticulationRate) ~ scale(Raw_first)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.00009 0.15379 -0.30246 0.29807 1.00003 13309 10411
## scaleRaw_first -0.32349 0.15719 -0.63269 -0.00992 1.00008 15489 11842
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.98480 0.11808 0.78712 1.24176 1.00008 13193 11424
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(ArtRate1)
bayes_R2(ArtRate1)## Estimate Est.Error Q2.5 Q97.5
## R2 0.1157661 0.07958506 0.001728084 0.2904245conditional_effects(ArtRate1)
ggplot(data, aes(tscore_first, ArticulationRate)) +
geom_point() +
geom_smooth()
ArtRate2 <- brm(scale(ArticulationRate) ~ scale(Raw_first) + scale(IndexCOCA_spoken_Frequency_Log_AW), data = data,
family = gaussian(),
prior = weak_prior,
iter = iter1, warmup = 1000, chains = 4, seed = 1234)
print(summary(ArtRate2), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(ArticulationRate) ~ scale(Raw_first) + scale(IndexCOCA_spoken_Frequency_Log_AW)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept -0.00073 0.15834 -0.30771 0.31118
## scaleRaw_first -0.25761 0.18304 -0.62123 0.09592
## scaleIndexCOCA_spoken_Frequency_Log_AW -0.12533 0.18474 -0.49038 0.23835
## Rhat Bulk_ESS Tail_ESS
## Intercept 1.00021 14891 11008
## scaleRaw_first 1.00007 13819 11335
## scaleIndexCOCA_spoken_Frequency_Log_AW 0.99988 12754 11538
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.98998 0.11973 0.78986 1.25491 1.00023 13827 10831
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(ArtRate2)
bayes_R2(ArtRate2)## Estimate Est.Error Q2.5 Q97.5
## R2 0.1418902 0.08181481 0.01174893 0.3156237conditional_effects(ArtRate2)
model_comp(ArtRate0, ArtRate1, ArtRate2)## [[1]]
## elpd_diff se_diff elpd_loo se_elpd_loo p_loo se_p_loo
## Model_1 0.0000000 0.0000000 -57.05483 4.013256 2.916145 0.6900494
## Model_2 -0.8417713 0.7124457 -57.89660 4.063434 3.843419 0.8495668
## Null_Model -1.2410619 2.3108760 -58.29590 4.493810 1.876090 0.5849525
## looic se_looic
## Model_1 114.1097 8.026512
## Model_2 115.7932 8.126868
## Null_Model 116.5918 8.987621
##
## [[2]]
## elpd_diff se_diff elpd_waic se_elpd_waic p_waic se_p_waic
## Model_1 0.0000000 0.0000000 -57.01941 4.003132 2.880722 0.6777534
## Model_2 -0.8029299 0.7090032 -57.82234 4.043105 3.769154 0.8254196
## Null_Model -1.2640034 2.3052202 -58.28341 4.487365 1.863608 0.5775197
## waic se_waic
## Model_1 114.0388 8.006264
## Model_2 115.6447 8.086210
## Null_Model 116.5668 8.974730
##
## [[3]]
##
## [[4]]
loo_model_weights(ArtRate0, ArtRate1, ArtRate2, model_names = NULL)## Method: stacking
## ------
## weight
## ArtRate0 0.246
## ArtRate1 0.754
## ArtRate2 0.000art_rate_ave <- posterior_average(ArtRate1, ArtRate2, weights = "stacking")
quantile(art_rate_ave$b_scaleRaw_first, prob = c(.025, .975))## 2.5% 97.5%
## -0.632694066 -0.009917758mcmc_areas(art_rate_ave, pars = "b_scaleRaw_first", prob = .95)+
labs(x = "Regression coefficent (std)") 
Silent pauses
get_prior(scale(SilentPause) ~ scale(Raw_first) + scale(tscore_first) + scale(IndexCOCA_spoken_Frequency_Log_AW), data = data,
family = gaussian())## prior class coef
## 1 b
## 2 b scaleIndexCOCA_spoken_Frequency_Log_AW
## 3 b scaleRaw_first
## 4 b scaletscore_first
## 5 student_t(3, -0.2, 2.5) Intercept
## 6 student_t(3, 0, 2.5) sigma
## group resp dpar nlpar bound
## 1
## 2
## 3
## 4
## 5
## 6silent0 <- brm(scale(SilentPause) ~ 1, data = data,
family = gaussian(),
iter = iter1, warmup = 1000, chains = 4, seed = 1234)silent1 <- brm(scale(SilentPause) ~ scale(Raw_first), data = data,
family = gaussian(),
prior = weak_prior,
iter = iter1, warmup = 1000, chains = 4, seed = 1234)
print(summary(silent1), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(SilentPause) ~ scale(Raw_first)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.00198 0.15494 -0.31139 0.30206 1.00022 14134 10491
## scaleRaw_first 0.34628 0.15620 0.04019 0.65551 1.00039 14131 11384
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.97562 0.11535 0.78213 1.23429 1.00023 12781 10127
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(silent1)
bayes_R2(silent1)## Estimate Est.Error Q2.5 Q97.5
## R2 0.1293257 0.08345256 0.003133629 0.308794conditional_effects(silent1)
silent2 <- brm(scale(SilentPause) ~ scale(Raw_first) + scale(IndexCOCA_spoken_Frequency_Log_AW), data = data,
family = gaussian(),
prior = weak_prior,
iter = iter1, warmup = 1000, chains = 4, seed = 1234)
print(summary(silent2), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(SilentPause) ~ scale(Raw_first) + scale(IndexCOCA_spoken_Frequency_Log_AW)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept -0.00319 0.15432 -0.30441 0.30084
## scaleRaw_first 0.38872 0.18371 0.02500 0.74222
## scaleIndexCOCA_spoken_Frequency_Log_AW -0.08082 0.18419 -0.44438 0.28142
## Rhat Bulk_ESS Tail_ESS
## Intercept 1.00016 15528 10989
## scaleRaw_first 1.00016 13399 12185
## scaleIndexCOCA_spoken_Frequency_Log_AW 1.00005 14162 11463
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.98625 0.11924 0.78583 1.25479 1.00020 13105 11159
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(silent2)
bayes_R2(silent2)## Estimate Est.Error Q2.5 Q97.5
## R2 0.1492143 0.08320292 0.0129555 0.3213162conditional_effects(silent2)
model_comp(silent0, silent1, silent2)## [[1]]
## elpd_diff se_diff elpd_loo se_elpd_loo p_loo se_p_loo looic
## Model_1 0.000000 0.000000 -56.55099 4.054563 2.644356 0.6887362 113.1020
## Model_2 -1.049256 0.600790 -57.60024 4.030346 3.745541 0.9388344 115.2005
## Null_Model -1.743217 2.062665 -58.29421 4.422236 1.853529 0.6492143 116.5884
## se_looic
## Model_1 8.109126
## Model_2 8.060692
## Null_Model 8.844472
##
## [[2]]
## elpd_diff se_diff elpd_waic se_elpd_waic p_waic se_p_waic
## Model_1 0.000000 0.0000000 -56.51679 4.039883 2.610157 0.6722935
## Model_2 -1.020433 0.5984865 -57.53722 4.007394 3.682519 0.9144548
## Null_Model -1.757910 2.0606844 -58.27470 4.409239 1.834023 0.6336745
## waic se_waic
## Model_1 113.0336 8.079766
## Model_2 115.0744 8.014787
## Null_Model 116.5494 8.818479
##
## [[3]]
##
## [[4]]
Bayesian stacking
loo_model_weights(silent0, silent1, silent2, model_names = NULL)## Method: stacking
## ------
## weight
## silent0 0.078
## silent1 0.922
## silent2 0.000Averaged posterior
silent_ave <- posterior_average(silent1, silent2, weights = "stacking")
quantile(silent_ave$b_scaleRaw_first, prob = c(.025, .975))## 2.5% 97.5%
## 0.04018646 0.65551027mcmc_areas(silent_ave, pars = "b_scaleRaw_first", prob = .95)+
labs(x = "Regression coefficent (std)") 
Filled pauses
get_prior(scale(FilledPause) ~ scale(Rawfreq) + scale(IndexCOCA_spoken_Frequency_Log_AW), data = data,
family = gaussian())## prior class coef
## 1 b
## 2 b scaleIndexCOCA_spoken_Frequency_Log_AW
## 3 b scaleRawfreq
## 4 student_t(3, -0.4, 2.5) Intercept
## 5 student_t(3, 0, 2.5) sigma
## group resp dpar nlpar bound
## 1
## 2
## 3
## 4
## 5FilledPause0 <- brm(scale(FilledPause) ~ 1, data = data,
family = gaussian(),
iter = iter1, warmup = 1000, chains = 4, seed = 1234)FilledPause1 <- brm(scale(FilledPause) ~ scale(Rawfreq), data = data,
family = gaussian(),
prior = weak_prior,
iter = iter1, warmup = 1000, chains = 4, seed = 1234)
print(summary(FilledPause1), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(FilledPause) ~ scale(Rawfreq)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.00199 0.15889 -0.31661 0.31154 1.00042 14265 11318
## scaleRawfreq -0.29118 0.15771 -0.59954 0.01948 0.99994 14852 11245
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.99700 0.11887 0.80014 1.26327 1.00013 14585 11828
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(FilledPause1)
bayes_R2(FilledPause1)## Estimate Est.Error Q2.5 Q97.5
## R2 0.09764099 0.07386499 0.0007376389 0.2642808conditional_effects(FilledPause1)
FilledPause2 <- brm(scale(FilledPause) ~ scale(Rawfreq) + scale(IndexCOCA_spoken_Frequency_Log_AW), data = data,
family = gaussian(),
prior = weak_prior,
iter = iter1, warmup = 1000, chains = 4, seed = 1234)
print(summary(FilledPause2), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(FilledPause) ~ scale(Rawfreq) + scale(IndexCOCA_spoken_Frequency_Log_AW)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept -0.00196 0.16248 -0.32379 0.31748
## scaleRawfreq -0.29053 0.18229 -0.65280 0.06313
## scaleIndexCOCA_spoken_Frequency_Log_AW 0.00577 0.18455 -0.35764 0.37398
## Rhat Bulk_ESS Tail_ESS
## Intercept 0.99989 13670 10435
## scaleRawfreq 1.00005 14010 11784
## scaleIndexCOCA_spoken_Frequency_Log_AW 1.00023 14376 12051
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.01079 0.12204 0.80642 1.28420 1.00027 13410 11329
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(FilledPause2)
bayes_R2(FilledPause2)## Estimate Est.Error Q2.5 Q97.5
## R2 0.1134629 0.07321546 0.006932863 0.2750717conditional_effects(FilledPause2)
model_comp(FilledPause0, FilledPause1, FilledPause2)## [[1]]
## elpd_diff se_diff elpd_loo se_elpd_loo p_loo se_p_loo
## Model_1 0.0000000 0.0000000 -57.84599 5.566585 3.383664 1.2370443
## Null_Model -0.3828682 2.4654512 -58.22886 4.255693 1.774056 0.4944716
## Model_2 -1.1206192 0.1919768 -58.96661 5.584871 4.321973 1.4838764
## looic se_looic
## Model_1 115.6920 11.133170
## Null_Model 116.4577 8.511385
## Model_2 117.9332 11.169743
##
## [[2]]
## elpd_diff se_diff elpd_waic se_elpd_waic p_waic se_p_waic
## Model_1 0.0000000 0.000000 -57.77300 5.524608 3.310672 1.1923489
## Null_Model -0.4443288 2.433204 -58.21733 4.250337 1.762525 0.4884505
## Model_2 -1.0536548 0.178447 -58.82666 5.515259 4.182016 1.4093829
## waic se_waic
## Model_1 115.5460 11.049216
## Null_Model 116.4347 8.500673
## Model_2 117.6533 11.030519
##
## [[3]]
##
## [[4]]
Bayesian stacking
loo_model_weights(FilledPause0, FilledPause1, FilledPause2, model_names = NULL)## Method: stacking
## ------
## weight
## FilledPause0 0.369
## FilledPause1 0.631
## FilledPause2 0.000averaged posterior
filled_ave <- posterior_average(FilledPause1, FilledPause2, weights = "stacking")
quantile(filled_ave$b_scaleRawfreq, prob = c(.025, .975))## 2.5% 97.5%
## -0.59954064 0.01948036mcmc_areas(filled_ave, pars = "b_scaleRawfreq", prob = .95)+
labs(x = "Regression coefficent (std)") 
Lexis
Richness
get_prior(scale(Richness) ~ scale(MI_first) + scale(Rawfreq) + scale(IndexCOCA_spoken_Frequency_Log_AW), data = data, family = gaussian())## prior class coef group
## 1 b
## 2 b scaleIndexCOCA_spoken_Frequency_Log_AW
## 3 b scaleMI_first
## 4 b scaleRawfreq
## 5 student_t(3, 0.2, 2.5) Intercept
## 6 student_t(3, 0, 2.5) sigma
## resp dpar nlpar bound
## 1
## 2
## 3
## 4
## 5
## 6Richness0 <- brm(scale(Richness) ~ 1, data = data,
family = gaussian(),
iter = iter1, warmup = 1000, chains = 4, seed =1234)Richness1 <- brm(scale(Richness) ~ scale(MI_first), data = data,
family = gaussian(),
prior = weak_prior,
iter = iter1, warmup = 1000, chains = 4, seed =1234)
print(summary(Richness1), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(Richness) ~ scale(MI_first)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.00016 0.15367 -0.30599 0.29952 1.00002 15782 11232
## scaleMI_first 0.35380 0.15315 0.05313 0.65514 1.00020 13973 10481
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.97205 0.11429 0.78056 1.22605 1.00018 13921 10483
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(Richness1)
bayes_R2(Richness1)## Estimate Est.Error Q2.5 Q97.5
## R2 0.133816 0.08371075 0.004042428 0.3106514conditional_effects(Richness1)
Richness2 <- brm(scale(Richness) ~ scale(MI_first) + scale(IndexCOCA_spoken_Frequency_Log_AW), data = data,
family = gaussian(),
prior = weak_prior,
iter = iter1, warmup = 1000, chains = 4)
print(summary(Richness2), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(Richness) ~ scale(MI_first) + scale(IndexCOCA_spoken_Frequency_Log_AW)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept 0.00158 0.14841 -0.29019 0.29214
## scaleMI_first 0.32033 0.14890 0.02482 0.61188
## scaleIndexCOCA_spoken_Frequency_Log_AW -0.29063 0.14946 -0.58401 0.00193
## Rhat Bulk_ESS Tail_ESS
## Intercept 1.00009 15712 10977
## scaleMI_first 1.00018 16705 11969
## scaleIndexCOCA_spoken_Frequency_Log_AW 1.00017 16407 11967
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.93674 0.11273 0.74586 1.18489 1.00036 14428 11986
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(Richness2)
bayes_R2(Richness2)## Estimate Est.Error Q2.5 Q97.5
## R2 0.2226223 0.09351495 0.04359286 0.3995478conditional_effects(Richness2)
model_comp(Richness0, Richness1, Richness2)## [[1]]
## elpd_diff se_diff elpd_loo se_elpd_loo p_loo se_p_loo looic
## Model_2 0.000000 0.000000 -55.10282 3.808640 3.077318 0.6817186 110.2056
## Model_1 -1.115905 1.896598 -56.21873 3.708801 2.341153 0.4944896 112.4375
## Null_Model -2.949545 2.935685 -58.05237 3.287924 1.471525 0.2569668 116.1047
## se_looic
## Model_2 7.617280
## Model_1 7.417602
## Null_Model 6.575848
##
## [[2]]
## elpd_diff se_diff elpd_waic se_elpd_waic p_waic se_p_waic
## Model_2 0.000000 0.000000 -55.06358 3.795063 3.038071 0.6666369
## Model_1 -1.135639 1.891523 -56.19922 3.702258 2.321640 0.4870916
## Null_Model -2.983141 2.928124 -58.04672 3.286238 1.465874 0.2551602
## waic se_waic
## Model_2 110.1272 7.590125
## Model_1 112.3984 7.404516
## Null_Model 116.0934 6.572476
##
## [[3]]
##
## [[4]]
Bayesian stacking
loo_model_weights(Richness0, Richness1, Richness2, model_names = NULL)## Method: stacking
## ------
## weight
## Richness0 0.137
## Richness1 0.000
## Richness2 0.863Average posterior
lexis_ave <- posterior_average(Richness1, Richness2, weights = "stacking")
quantile(lexis_ave$b_scaleMI_first, prob = c(.025, .975))## 2.5% 97.5%
## 0.0277728 0.6167806mcmc_areas(lexis_ave, pars = "b_scaleMI_first", prob = .95)+
labs(x = "Regression coefficent (std)") 
Frequency
get_prior(scale(COCA_spoken_Frequency_Log_AW) ~ scale(MI) + scale(IndexCOCA_spoken_Frequency_Log_AW), data = data, family = gaussian())## prior class coef group
## 1 b
## 2 b scaleIndexCOCA_spoken_Frequency_Log_AW
## 3 b scaleMI
## 4 student_t(3, 0.1, 2.5) Intercept
## 5 student_t(3, 0, 2.5) sigma
## resp dpar nlpar bound
## 1
## 2
## 3
## 4
## 5freq_first0 <- brm(scale(COCA_spoken_Frequency_Log_AW) ~ 1, data = data,
family = gaussian(),
iter = iter1, warmup = 1000, chains = 4, seed =1234)freq_total0 <- brm(scale(COCA_spoken_Frequency_Log_AW) ~ 1 , data = data,
family = gaussian(),
iter = iter1, warmup = 1000, chains = 4, seed =1234)freq_first1 <- brm(scale(COCA_spoken_Frequency_Log_AW) ~ scale(MI_first) , data = data,
family = gaussian(),
prior = weak_prior,
iter = iter1, warmup = 1000, chains = 4, seed =1234)
print(summary(freq_first1), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(COCA_spoken_Frequency_Log_AW) ~ scale(MI_first)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.00226 0.15577 -0.30047 0.30766 1.00030 14226 11161
## scaleMI_first -0.32890 0.15700 -0.63796 -0.01812 1.00033 14454 11200
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.98269 0.11760 0.78317 1.24420 0.99990 12395 11725
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(freq_first1)
bayes_R2(freq_first1)## Estimate Est.Error Q2.5 Q97.5
## R2 0.1189594 0.08090103 0.00194713 0.2950063conditional_effects(freq_first1)
freq_total1 <- brm(scale(COCA_spoken_Frequency_Log_AW) ~ scale(MI) , data = data,
family = gaussian(),
prior = weak_prior,
iter = iter1, warmup = 1000, chains = 4, seed =1234)
print(summary(freq_total1), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(COCA_spoken_Frequency_Log_AW) ~ scale(MI)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.00124 0.15679 -0.30896 0.30922 1.00015 14866 10654
## scaleMI -0.31906 0.15995 -0.63854 -0.00514 1.00072 14089 11442
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.98698 0.11877 0.78851 1.25016 1.00012 13754 11128
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(freq_total1)
bayes_R2(freq_total1)## Estimate Est.Error Q2.5 Q97.5
## R2 0.1137115 0.0803816 0.001334179 0.2931654conditional_effects(freq_total1)
freq_first2 <- brm(scale(COCA_spoken_Frequency_Log_AW) ~ scale(MI_first) + scale(IndexCOCA_spoken_Frequency_Log_AW) , data = data,
family = gaussian(),
prior = weak_prior,
iter = iter1, warmup = 1000, chains = 4, seed =1234)
print(summary(freq_first2), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(COCA_spoken_Frequency_Log_AW) ~ scale(MI_first) + scale(IndexCOCA_spoken_Frequency_Log_AW)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept -0.00055 0.14500 -0.29324 0.28609
## scaleMI_first -0.28960 0.14667 -0.57818 -0.00182
## scaleIndexCOCA_spoken_Frequency_Log_AW 0.35879 0.14761 0.06758 0.64484
## Rhat Bulk_ESS Tail_ESS
## Intercept 1.00052 16627 11206
## scaleMI_first 1.00020 16786 11897
## scaleIndexCOCA_spoken_Frequency_Log_AW 1.00020 16811 11323
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.91792 0.11336 0.72988 1.16895 1.00012 14758 11183
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(freq_first2)
conditional_effects(freq_first2)
bayes_R2(freq_first2)## Estimate Est.Error Q2.5 Q97.5
## R2 0.2483606 0.09531583 0.06089122 0.4249321freq_total2 <- brm(scale(COCA_spoken_Frequency_Log_AW) ~ scale(MI) + scale(IndexCOCA_spoken_Frequency_Log_AW), data = data,
family = gaussian(),
prior = weak_prior,
iter = iter1, warmup = 1000, chains = 4, seed =1234)
print(summary(freq_total2), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(COCA_spoken_Frequency_Log_AW) ~ scale(MI) + scale(IndexCOCA_spoken_Frequency_Log_AW)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept -0.00073 0.14962 -0.29472 0.29264
## scaleMI -0.22574 0.15792 -0.53732 0.08636
## scaleIndexCOCA_spoken_Frequency_Log_AW 0.32668 0.15660 0.01652 0.62886
## Rhat Bulk_ESS Tail_ESS
## Intercept 1.00043 16412 11589
## scaleMI 1.00011 15052 11056
## scaleIndexCOCA_spoken_Frequency_Log_AW 1.00014 15466 11744
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.93931 0.11214 0.75097 1.19175 0.99997 15055 11395
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(freq_total2)
bayes_R2(freq_total2)## Estimate Est.Error Q2.5 Q97.5
## R2 0.2170681 0.09273908 0.04170135 0.3916281conditional_effects(freq_total2)
model_comp(freq_first0, freq_first1, freq_first2)## [[1]]
## elpd_diff se_diff elpd_loo se_elpd_loo p_loo se_p_loo looic
## Model_2 0.000000 0.000000 -55.46093 6.069648 4.842106 1.9653494 110.9219
## Model_1 -2.148586 2.700473 -57.60951 7.053405 3.893989 1.9614126 115.2190
## Null_Model -3.140519 2.769052 -58.60145 5.523183 2.348885 0.8977871 117.2029
## se_looic
## Model_2 12.13930
## Model_1 14.10681
## Null_Model 11.04637
##
## [[2]]
## elpd_diff se_diff elpd_waic se_elpd_waic p_waic se_p_waic
## Model_2 0.000000 0.000000 -55.28399 5.960505 4.665168 1.8440044
## Model_1 -2.244599 2.716633 -57.52859 6.995822 3.813064 1.8991506
## Null_Model -3.288145 2.727782 -58.57214 5.506132 2.319574 0.8782678
## waic se_waic
## Model_2 110.5680 11.92101
## Model_1 115.0572 13.99164
## Null_Model 117.1443 11.01226
##
## [[3]]
##
## [[4]]
Bayesian stacking
loo_model_weights(freq_first0, freq_first1, freq_first2)## Method: stacking
## ------
## weight
## freq_first0 0.000
## freq_first1 0.177
## freq_first2 0.823Averaged posterior
freq_ave <- posterior_average(freq_first1, freq_first2, weights = "stacking")
quantile(freq_ave$b_scaleMI_first, prob = c(.025, .975))## 2.5% 97.5%
## -0.592263176 -0.002254059mcmc_areas(freq_ave, pars = "b_scaleMI_first", prob = .95)+
labs(x = "Regression coefficent (std)") 
model_comp(freq_total0, freq_total1, freq_total2)## [[1]]
## elpd_diff se_diff elpd_loo se_elpd_loo p_loo se_p_loo looic
## Model_2 0.000000 0.000000 -56.18234 5.680600 4.513436 1.6633735 112.3647
## Model_1 -1.289846 2.617130 -57.47218 6.409359 3.449622 1.5875915 114.9444
## Null_Model -2.419109 2.711988 -58.60145 5.523183 2.348885 0.8977871 117.2029
## se_looic
## Model_2 11.36120
## Model_1 12.81872
## Null_Model 11.04637
##
## [[2]]
## elpd_diff se_diff elpd_waic se_elpd_waic p_waic se_p_waic
## Model_2 0.000000 0.000000 -56.06766 5.614297 4.398758 1.5881553
## Model_1 -1.313396 2.609087 -57.38106 6.339455 3.358495 1.5109828
## Null_Model -2.504475 2.698814 -58.57214 5.506132 2.319574 0.8782678
## waic se_waic
## Model_2 112.1353 11.22859
## Model_1 114.7621 12.67891
## Null_Model 117.1443 11.01226
##
## [[3]]
##
## [[4]]
loo_model_weights(freq_total0, freq_total1, freq_total2)## Method: stacking
## ------
## weight
## freq_total0 0.000
## freq_total1 0.273
## freq_total2 0.727freq_ave2 <- posterior_average(freq_total1, freq_total2, weights = "stacking")
quantile(freq_ave2$b_scaleMI, prob = c(.025, .975))## 2.5% 97.5%
## -0.58073173 0.06741606ggplot(freq_ave2, aes(x = b_scaleMI, y = ..density..)) +
geom_density()
mcmc_areas(freq_ave2, pars = "b_scaleMI", prob = .95)+
labs(x = "Regression coefficent (std)") 
Range
get_prior(scale(COCA_spoken_Range_Log_AW) ~ scale(MI) + scale(IndexCOCA_spoken_Frequency_Log_AW) , data = data, family = gaussian())## prior class coef group
## 1 b
## 2 b scaleIndexCOCA_spoken_Frequency_Log_AW
## 3 b scaleMI
## 4 student_t(3, 0.2, 2.5) Intercept
## 5 student_t(3, 0, 2.5) sigma
## resp dpar nlpar bound
## 1
## 2
## 3
## 4
## 5range0 <- brm(scale(COCA_spoken_Range_Log_AW) ~ 1 , data = data,
family = gaussian(),
iter = iter1, warmup = 1000, chains = 4, seed =1234)range1 <- brm(scale(COCA_spoken_Range_Log_AW) ~ scale(MI) , data = data,
family = gaussian(),
prior = weak_prior,
iter = iter1, warmup = 1000, chains = 4, seed =1234)
print(summary(range1), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(COCA_spoken_Range_Log_AW) ~ scale(MI)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.00113 0.15651 -0.31315 0.30470 1.00007 12618 10709
## scaleMI -0.30656 0.15719 -0.61919 0.00059 1.00020 14399 10856
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.99008 0.11776 0.79252 1.25177 1.00032 12852 11559
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(range1)
bayes_R2(range1)## Estimate Est.Error Q2.5 Q97.5
## R2 0.1059115 0.07681136 0.001130617 0.2786825conditional_effects(range1)
range2 <- brm(scale(COCA_spoken_Range_Log_AW) ~ scale(MI) + scale(IndexCOCA_spoken_Frequency_Log_AW) , data = data,
family = gaussian(),
prior = weak_prior,
iter = 5000, warmup = 1000, chains = 4, seed =1234)
print(summary(range2), digits = 5)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: scale(COCA_spoken_Range_Log_AW) ~ scale(MI) + scale(IndexCOCA_spoken_Frequency_Log_AW)
## Data: data (Number of observations: 40)
## Samples: 4 chains, each with iter = 5000; warmup = 1000; thin = 1;
## total post-warmup samples = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept 0.00001 0.15525 -0.30441 0.30154
## scaleMI -0.24158 0.16041 -0.55621 0.07428
## scaleIndexCOCA_spoken_Frequency_Log_AW 0.21625 0.16248 -0.09985 0.53578
## Rhat Bulk_ESS Tail_ESS
## Intercept 0.99998 16713 12370
## scaleMI 1.00009 14839 10816
## scaleIndexCOCA_spoken_Frequency_Log_AW 1.00028 15676 11707
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.97989 0.11847 0.78025 1.24317 1.00048 14547 11944
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).plot(range2)
bayes_R2(range2)## Estimate Est.Error Q2.5 Q97.5
## R2 0.1593404 0.08457742 0.01630894 0.331478conditional_effects(range2)
model_comp(range0, range1, range2)## [[1]]
## elpd_diff se_diff elpd_loo se_elpd_loo p_loo se_p_loo
## Model_1 0.0000000 0.000000 -57.77425 6.692283 3.639436 1.4085823
## Model_2 -0.4653911 2.069652 -58.23964 6.784503 5.158969 1.9704319
## Null_Model -0.8113045 2.161109 -58.58556 5.592533 2.355700 0.8383746
## looic se_looic
## Model_1 115.5485 13.38457
## Model_2 116.4793 13.56901
## Null_Model 117.1711 11.18507
##
## [[2]]
## elpd_diff se_diff elpd_waic se_elpd_waic p_waic se_p_waic
## Model_1 0.0000000 0.000000 -57.67642 6.631913 3.541602 1.3405229
## Model_2 -0.4258103 2.042399 -58.10223 6.715009 5.021554 1.8962687
## Null_Model -0.8809419 2.122003 -58.55736 5.577541 2.327504 0.8216292
## waic se_waic
## Model_1 115.3528 13.26383
## Model_2 116.2045 13.43002
## Null_Model 117.1147 11.15508
##
## [[3]]
##
## [[4]]
### Bayesian stacking
loo_model_weights(range0, range1, range2, model_names = NULL)## Method: stacking
## ------
## weight
## range0 0.236
## range1 0.388
## range2 0.376Averaged posterior
range_ave <- posterior_average(range1, range2, weights = "stacking")
quantile(range_ave$b_scaleMI, prob = c(.025, .975))## 2.5% 97.5%
## -0.59471863 0.03757488mcmc_areas(range_ave, pars = "b_scaleMI", prob = .95)+
labs(x = "Regression coefficent (std)") 
Sensitivity analysis (Code adapted from Saito et al. [2020])
Defining functions for sensitivity analysis (some parts have to be modified for other dataset)
sa.func <- function(formula) {
sds <- c(0.8, 0.9, 1:3, 10)
sa <- vector("list", length(sds) + 1)
for (i in seq(length(sds))) {
# SD = 1
iter <- sds[i]
student_t.prior <- prior(student_t(3, 0, iter), class = "b")
stanvars <- stanvar(iter, name = "iter")
m <- brm(formula = formula,
data = data,
family = gaussian(),
prior = student_t.prior,
iter = iter1,
stanvars = stanvars,
warmup = 1000,
chains = 4,
seed =1234)
sa[[i]] <- mcmc_intervals_data(m)[2,c(5,7,9)]
}
## adding flat prior
flat.m <- brm(
formula = formula,
data = data,
family = gaussian(),
iter = iter1,
stanvars = stanvars,
warmup = 1000,
chains = 4,
seed =1234)
sa[[length(sa)]] <- mcmc_intervals_data(flat.m)[2,c(5,7,9)]
return(sa)
}
generate.as.df <- function(sa, outcome) {
sa.df <- sa %>%
lapply(data.frame) %>%
bind_rows %>%
mutate(
outcome = rep(outcome ,length(sa)),
prior = c(paste("SD =", c("0.8", "0.9", 1:3, 10)), "Flat") %>% factor(levels = c(paste("SD =", c("0.8", "0.9", 1:3, 10)), "Flat"))
) %>%
rename(estimate = 2, lower = 1, upper = 3) %>%
mutate(
lower.posneg = ifelse(lower < 0, 0, 1) %>% factor,
upper.posneg = ifelse(upper < 0, 0, 1) %>% factor
) %>%
as_tibble
return(sa.df)
}
sa.plot <- function(as.df) {
sa.gg <- ggplot(as.df , aes(prior, estimate)) +
geom_pointrange(aes(ymin = lower, ymax = upper)) +
geom_hline(yintercept = 0, linetype = 2, alpha = 0.7) +
geom_text(aes(y = lower, label = lower %>% round(2) %>% format(nsmall = 2), color = lower.posneg), vjust = 1, size = 3) +
geom_text(aes(y = upper, label = upper %>% round(2) %>% format(nsmall = 2), color = upper.posneg), vjust = 1, size = 3) +
scale_y_continuous(breaks = c(-1, 0, 1)) +
scale_color_manual(values = c('red', 'blue')) +
coord_flip(ylim = c(-1.2, 1.2)) +
theme_bw() +
theme(
text = element_text(size = 13),
legend.position = "none"
) +
labs(title = paste("Sensitivity analysis on", as.df$outcome[1]), x = "Prior Distribution", y = "Posterior Mean and 95% Credible Interval")
return(sa.gg)
}Fluency ratings
sa.fluency <- sa.func(formula = scale(Fluency) ~ scale(Raw_first))
as.fluency.df <- generate.as.df(sa.fluency, "Fluency rating")
sa.plot(as.fluency.df)
Articulation rate
sa.articulation.rate <- sa.func(formula = scale(ArticulationRate) ~ scale(Raw_first))
as.articulationrate.df <- generate.as.df(sa.fluency, "Articulation Rate")
sa.plot(as.articulationrate.df)
Silent pause ratio
sa.silentpause <- sa.func(formula = scale(SilentPause) ~ scale(Raw_first))
as.silentpause.df <- generate.as.df(sa.silentpause, "Silent pause ratio")
sa.plot(as.silentpause.df)
Filled pause ratio
sa.filledpause <- sa.func(formula = scale(FilledPause) ~ scale(Rawfreq))
as.filledpause.df <- generate.as.df(sa.filledpause, "Filled pause ratio")
sa.plot(as.filledpause.df)
Lexical richness
sa.lexicalrichness <- sa.func(formula = scale(Richness) ~ scale(MI_first) + scale(IndexCOCA_spoken_Frequency_Log_AW))
as.lexicalrichness.df <- generate.as.df(sa.lexicalrichness, "Lexical richness")
sa.plot(as.lexicalrichness.df)
Lexical Frequency
sa.frequency <- sa.func(formula = scale(COCA_spoken_Frequency_Log_AW) ~ scale(MI_first) + scale(IndexCOCA_spoken_Frequency_Log_AW) )
as.frequency.df <- generate.as.df(sa.frequency, "Articulation Rate")
sa.plot(as.frequency.df)
Range
sa.range <- sa.func(formula = scale(COCA_spoken_Range_Log_AW) ~ scale(MI) + scale(IndexCOCA_spoken_Frequency_Log_AW) )
as.range.df <- generate.as.df(sa.range, "Range")
sa.plot(as.range.df)
sa.gg.fluency <- ggplot(as.fluency.df , aes(prior, estimate)) +
geom_pointrange(aes(ymin = lower, ymax = upper)) +
geom_hline(yintercept = 0, linetype = 2, alpha = 0.7) +
geom_text(aes(y = lower, label = lower %>% round(2) %>% format(nsmall = 2), color = lower.posneg), vjust = 1, size = 3) +
geom_text(aes(y = upper, label = upper %>% round(2) %>% format(nsmall = 2), color = upper.posneg), vjust = 1, size = 3) +
scale_y_continuous(breaks = c(-1, 0, 1)) +
scale_color_manual(values = c('red', 'blue')) +
coord_flip(ylim = c(-1.2, 1.2)) +
theme_bw() +
theme(
text = element_text(size = 13),
legend.position = "none",
axis.title = element_blank()
) +
labs(title = 'Fluency rating')
sa.gg.art <- ggplot(as.articulationrate.df , aes(prior, estimate)) +
geom_pointrange(aes(ymin = lower, ymax = upper)) +
geom_hline(yintercept = 0, linetype = 2, alpha = 0.7) +
geom_text(aes(y = lower, label = lower %>% round(2) %>% format(nsmall = 2), color = lower.posneg), vjust = 1, size = 3) +
geom_text(aes(y = upper, label = upper %>% round(2) %>% format(nsmall = 2), color = upper.posneg), vjust = 1, size = 3) +
scale_y_continuous(breaks = c(-1, 0, 1)) +
scale_color_manual(values = c('red', 'blue')) +
coord_flip(ylim = c(-1.2, 1.2)) +
theme_bw() +
theme(
text = element_text(size = 13),
legend.position = "none",
axis.title = element_blank()
) +
labs(title = 'Articulation rate')
sa.gg.silent <- ggplot(as.silentpause.df , aes(prior, estimate)) +
geom_pointrange(aes(ymin = lower, ymax = upper)) +
geom_hline(yintercept = 0, linetype = 2, alpha = 0.7) +
geom_text(aes(y = lower, label = lower %>% round(2) %>% format(nsmall = 2), color = lower.posneg), vjust = 1, size = 3) +
geom_text(aes(y = upper, label = upper %>% round(2) %>% format(nsmall = 2), color = upper.posneg), vjust = 1, size = 3) +
scale_y_continuous(breaks = c(-1, 0, 1)) +
scale_color_manual(values = c('red', 'blue')) +
coord_flip(ylim = c(-1.2, 1.2)) +
theme_bw() +
theme(
text = element_text(size = 13),
legend.position = "none",
axis.title = element_blank()
) +
labs(title = 'Silent pause ratio')
sa.gg.filled <- ggplot(as.filledpause.df , aes(prior, estimate)) +
geom_pointrange(aes(ymin = lower, ymax = upper)) +
geom_hline(yintercept = 0, linetype = 2, alpha = 0.7) +
geom_text(aes(y = lower, label = lower %>% round(2) %>% format(nsmall = 2), color = lower.posneg), vjust = 1, size = 3) +
geom_text(aes(y = upper, label = upper %>% round(2) %>% format(nsmall = 2), color = upper.posneg), vjust = 1, size = 3) +
scale_y_continuous(breaks = c(-1, 0, 1)) +
scale_color_manual(values = c('red', 'blue')) +
coord_flip(ylim = c(-1.2, 1.2)) +
theme_bw() +
theme(
text = element_text(size = 13),
legend.position = "none",
axis.title = element_blank()
) +
labs(title = 'Filled pause ratio')
sa.gg.lexicalrichness<- ggplot(as.lexicalrichness.df , aes(prior, estimate)) +
geom_pointrange(aes(ymin = lower, ymax = upper)) +
geom_hline(yintercept = 0, linetype = 2, alpha = 0.7) +
geom_text(aes(y = lower, label = lower %>% round(2) %>% format(nsmall = 2), color = lower.posneg), vjust = 1, size = 3) +
geom_text(aes(y = upper, label = upper %>% round(2) %>% format(nsmall = 2), color = upper.posneg), vjust = 1, size = 3) +
scale_y_continuous(breaks = c(-1, 0, 1)) +
scale_color_manual(values = c('red', 'blue')) +
coord_flip(ylim = c(-1.2, 1.2)) +
theme_bw() +
theme(
text = element_text(size = 13),
legend.position = "none",
axis.title = element_blank()
) +
labs(title = 'Richness rating')
sa.gg.frequency <- ggplot(as.frequency.df , aes(prior, estimate)) +
geom_pointrange(aes(ymin = lower, ymax = upper)) +
geom_hline(yintercept = 0, linetype = 2, alpha = 0.7) +
geom_text(aes(y = lower, label = lower %>% round(2) %>% format(nsmall = 2), color = lower.posneg), vjust = 1, size = 3) +
geom_text(aes(y = upper, label = upper %>% round(2) %>% format(nsmall = 2), color = upper.posneg), vjust = 1, size = 3) +
scale_y_continuous(breaks = c(-1, 0, 1)) +
scale_color_manual(values = c('red', 'blue')) +
coord_flip(ylim = c(-1.2, 1.2)) +
theme_bw() +
theme(
text = element_text(size = 13),
legend.position = "none",
axis.title = element_blank()
) +
labs(title = 'Frequency')
sa.gg.range <- ggplot(as.range.df , aes(prior, estimate)) +
geom_pointrange(aes(ymin = lower, ymax = upper)) +
geom_hline(yintercept = 0, linetype = 2, alpha = 0.7) +
geom_text(aes(y = lower, label = lower %>% round(2) %>% format(nsmall = 2), color = lower.posneg), vjust = 1, size = 3) +
geom_text(aes(y = upper, label = upper %>% round(2) %>% format(nsmall = 2), color = upper.posneg), vjust = 1, size = 3) +
scale_y_continuous(breaks = c(-1, 0, 1)) +
scale_color_manual(values = c('red', 'blue')) +
coord_flip(ylim = c(-1.2, 1.2)) +
theme_bw() +
theme(
text = element_text(size = 13),
legend.position = "none",
axis.title = element_blank()
) +
labs(title = 'Range')
grid.arrange(sa.gg.fluency,sa.gg.art, sa.gg.silent, sa.gg.filled, sa.gg.lexicalrichness, sa.gg.frequency,sa.gg.range, ncol = 2,
top = "Sensitivity analysis",
left = "Prior Distribution",
bottom = "Posterior Mean and 95% Credible Interval")